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Knot Atlas - User contributions [en]
2026-04-21T09:48:28Z
User contributions
MediaWiki 1.39.6
https://katlas.org/index.php?title=10_52&diff=1693822
10 52
2009-05-27T08:56:39Z
<p>DarerRacel: </p>
<hr />
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<!-- WARNING! WARNING! WARNING!<br />
<!-- This page was generated from the splice base [[Rolfsen_Splice_Base]]. Please do not edit!<br />
<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)<br />
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Rolfsen_Splice_Base]]. --><br />
<!-- --><br />
<!-- --><br />
{{Rolfsen Knot Page|<br />
n = 10 |<br />
k = 52 |<br />
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,2,-10,3,-1,9,-2,5,-6,7,-8,10,-3,4,-5,8,-7,6,-4/goTop.html |<br />
braid_table = <table cellspacing=0 cellpadding=0 border=0><br />
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr><br />
</table> |<br />
braid_crossings = 11 |<br />
braid_width = 4 |<br />
braid_index = 4 |<br />
same_alexander = [[10_23]], |<br />
same_jones = |<br />
khovanov_table = <table border=1><br />
<tr align=center><br />
<td width=13.3333%><table cellpadding=0 cellspacing=0><br />
<tr><td>\</td><td>&nbsp;</td><td>r</td></tr><br />
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr><br />
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr><br />
</table></td><br />
<td width=6.66667%>-5</td ><td width=6.66667%>-4</td ><td width=6.66667%>-3</td ><td width=6.66667%>-2</td ><td width=6.66667%>-1</td ><td width=6.66667%>0</td ><td width=6.66667%>1</td ><td width=6.66667%>2</td ><td width=6.66667%>3</td ><td width=6.66667%>4</td ><td width=6.66667%>5</td ><td width=13.3333%>&chi;</td></tr><br />
<tr align=center><td>13</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>-1</td></tr><br />
<tr align=center><td>11</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-3</td></tr><br />
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr><br />
<tr align=center><td>-5</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr><br />
<tr align=center><td>-7</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>-9</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
</table> |<br />
coloured_jones_2 = <math>q^{17}-3 q^{16}+3 q^{15}+4 q^{14}-15 q^{13}+14 q^{12}+9 q^{11}-37 q^{10}+31 q^9+17 q^8-60 q^7+41 q^6+30 q^5-73 q^4+35 q^3+43 q^2-70 q+20+46 q^{-1} -52 q^{-2} +3 q^{-3} +37 q^{-4} -28 q^{-5} -6 q^{-6} +21 q^{-7} -9 q^{-8} -6 q^{-9} +7 q^{-10} - q^{-11} -2 q^{-12} + q^{-13} </math> |<br />
coloured_jones_3 = <math>-q^{33}+3 q^{32}-3 q^{31}-q^{30}+3 q^{29}+4 q^{28}-9 q^{27}-4 q^{26}+19 q^{25}+2 q^{24}-35 q^{23}+5 q^{22}+53 q^{21}-9 q^{20}-85 q^{19}+20 q^{18}+117 q^{17}-22 q^{16}-156 q^{15}+18 q^{14}+190 q^{13}-6 q^{12}-210 q^{11}-24 q^{10}+228 q^9+47 q^8-216 q^7-88 q^6+211 q^5+107 q^4-173 q^3-145 q^2+155 q+150-108 q^{-1} -169 q^{-2} +80 q^{-3} +160 q^{-4} -35 q^{-5} -155 q^{-6} +6 q^{-7} +130 q^{-8} +26 q^{-9} -105 q^{-10} -43 q^{-11} +73 q^{-12} +49 q^{-13} -41 q^{-14} -48 q^{-15} +20 q^{-16} +34 q^{-17} -2 q^{-18} -24 q^{-19} -2 q^{-20} +11 q^{-21} +5 q^{-22} -6 q^{-23} -2 q^{-24} + q^{-25} +2 q^{-26} - q^{-27} </math> |<br />
coloured_jones_4 = <math>q^{54}-3 q^{53}+3 q^{52}+q^{51}-6 q^{50}+8 q^{49}-9 q^{48}+10 q^{47}-2 q^{46}-22 q^{45}+36 q^{44}-19 q^{43}+15 q^{42}-20 q^{41}-51 q^{40}+111 q^{39}-21 q^{38}-8 q^{37}-91 q^{36}-82 q^{35}+286 q^{34}+19 q^{33}-92 q^{32}-277 q^{31}-149 q^{30}+581 q^{29}+185 q^{28}-178 q^{27}-595 q^{26}-343 q^{25}+880 q^{24}+481 q^{23}-120 q^{22}-888 q^{21}-673 q^{20}+978 q^{19}+743 q^{18}+122 q^{17}-958 q^{16}-977 q^{15}+825 q^{14}+792 q^{13}+416 q^{12}-776 q^{11}-1114 q^{10}+543 q^9+643 q^8+630 q^7-478 q^6-1085 q^5+249 q^4+407 q^3+749 q^2-163 q-955-23 q^{-1} +149 q^{-2} +778 q^{-3} +137 q^{-4} -728 q^{-5} -233 q^{-6} -134 q^{-7} +672 q^{-8} +375 q^{-9} -396 q^{-10} -294 q^{-11} -378 q^{-12} +404 q^{-13} +442 q^{-14} -49 q^{-15} -163 q^{-16} -454 q^{-17} +88 q^{-18} +300 q^{-19} +141 q^{-20} +39 q^{-21} -321 q^{-22} -88 q^{-23} +84 q^{-24} +123 q^{-25} +134 q^{-26} -125 q^{-27} -83 q^{-28} -30 q^{-29} +31 q^{-30} +97 q^{-31} -17 q^{-32} -23 q^{-33} -32 q^{-34} -11 q^{-35} +35 q^{-36} +3 q^{-37} +2 q^{-38} -9 q^{-39} -9 q^{-40} +7 q^{-41} + q^{-42} +2 q^{-43} - q^{-44} -2 q^{-45} + q^{-46} </math> |<br />
coloured_jones_5 = <math>-q^{80}+3 q^{79}-3 q^{78}-q^{77}+6 q^{76}-5 q^{75}-3 q^{74}+8 q^{73}-4 q^{72}-q^{71}+8 q^{70}-12 q^{69}-11 q^{68}+21 q^{67}+14 q^{66}-5 q^{65}-22 q^{64}-34 q^{63}+7 q^{62}+75 q^{61}+66 q^{60}-59 q^{59}-162 q^{58}-103 q^{57}+133 q^{56}+334 q^{55}+192 q^{54}-276 q^{53}-619 q^{52}-366 q^{51}+470 q^{50}+1080 q^{49}+647 q^{48}-674 q^{47}-1678 q^{46}-1161 q^{45}+821 q^{44}+2461 q^{43}+1860 q^{42}-832 q^{41}-3231 q^{40}-2808 q^{39}+583 q^{38}+3964 q^{37}+3871 q^{36}-94 q^{35}-4443 q^{34}-4915 q^{33}-655 q^{32}+4597 q^{31}+5812 q^{30}+1530 q^{29}-4432 q^{28}-6383 q^{27}-2373 q^{26}+3910 q^{25}+6625 q^{24}+3128 q^{23}-3295 q^{22}-6482 q^{21}-3611 q^{20}+2501 q^{19}+6137 q^{18}+3925 q^{17}-1853 q^{16}-5565 q^{15}-3996 q^{14}+1130 q^{13}+5005 q^{12}+4030 q^{11}-634 q^{10}-4339 q^9-3928 q^8-17 q^7+3764 q^6+3906 q^5+473 q^4-3070 q^3-3745 q^2-1143 q+2397+3633 q^{-1} +1616 q^{-2} -1573 q^{-3} -3292 q^{-4} -2185 q^{-5} +740 q^{-6} +2871 q^{-7} +2475 q^{-8} +147 q^{-9} -2186 q^{-10} -2648 q^{-11} -918 q^{-12} +1415 q^{-13} +2448 q^{-14} +1536 q^{-15} -529 q^{-16} -2055 q^{-17} -1844 q^{-18} -246 q^{-19} +1386 q^{-20} +1846 q^{-21} +874 q^{-22} -681 q^{-23} -1559 q^{-24} -1177 q^{-25} +13 q^{-26} +1052 q^{-27} +1218 q^{-28} +471 q^{-29} -529 q^{-30} -995 q^{-31} -681 q^{-32} +44 q^{-33} +644 q^{-34} +702 q^{-35} +239 q^{-36} -302 q^{-37} -520 q^{-38} -362 q^{-39} +21 q^{-40} +326 q^{-41} +328 q^{-42} +110 q^{-43} -121 q^{-44} -234 q^{-45} -155 q^{-46} +16 q^{-47} +120 q^{-48} +120 q^{-49} +50 q^{-50} -50 q^{-51} -81 q^{-52} -39 q^{-53} +2 q^{-54} +32 q^{-55} +40 q^{-56} +8 q^{-57} -19 q^{-58} -13 q^{-59} -8 q^{-60} -2 q^{-61} +11 q^{-62} +7 q^{-63} -3 q^{-64} -2 q^{-65} - q^{-66} -2 q^{-67} + q^{-68} +2 q^{-69} - q^{-70} </math> |<br />
coloured_jones_6 = <math>q^{111}-3 q^{110}+3 q^{109}+q^{108}-6 q^{107}+5 q^{106}+4 q^{104}-14 q^{103}+7 q^{102}+15 q^{101}-26 q^{100}+18 q^{99}+5 q^{98}-5 q^{97}-37 q^{96}+22 q^{95}+59 q^{94}-62 q^{93}+23 q^{92}-6 q^{91}-42 q^{90}-55 q^{89}+123 q^{88}+192 q^{87}-164 q^{86}-100 q^{85}-170 q^{84}-129 q^{83}+115 q^{82}+596 q^{81}+612 q^{80}-468 q^{79}-798 q^{78}-963 q^{77}-422 q^{76}+901 q^{75}+2241 q^{74}+1962 q^{73}-996 q^{72}-2896 q^{71}-3549 q^{70}-1659 q^{69}+2553 q^{68}+6269 q^{67}+5743 q^{66}-877 q^{65}-6779 q^{64}-9469 q^{63}-5700 q^{62}+3925 q^{61}+12961 q^{60}+13693 q^{59}+2283 q^{58}-10692 q^{57}-18675 q^{56}-14467 q^{55}+1913 q^{54}+19644 q^{53}+25210 q^{52}+10645 q^{51}-10654 q^{50}-27467 q^{49}-26739 q^{48}-5805 q^{47}+21506 q^{46}+35577 q^{45}+22409 q^{44}-4323 q^{43}-30514 q^{42}-37060 q^{41}-16824 q^{40}+16488 q^{39}+39319 q^{38}+31754 q^{37}+5350 q^{36}-26325 q^{35}-40357 q^{34}-25325 q^{33}+8043 q^{32}+35758 q^{31}+34436 q^{30}+12861 q^{29}-18752 q^{28}-36938 q^{27}-28088 q^{26}+1142 q^{25}+29006 q^{24}+31710 q^{23}+16027 q^{22}-12149 q^{21}-31018 q^{20}-27007 q^{19}-2896 q^{18}+22750 q^{17}+27575 q^{16}+16999 q^{15}-7174 q^{14}-25518 q^{13}-25488 q^{12}-6194 q^{11}+17092 q^{10}+24019 q^9+18392 q^8-1873 q^7-19974 q^6-24460 q^5-10547 q^4+10191 q^3+19883 q^2+20150 q+4894-12517 q^{-1} -22066 q^{-2} -15065 q^{-3} +1389 q^{-4} +13095 q^{-5} +19786 q^{-6} +11592 q^{-7} -2785 q^{-8} -16031 q^{-9} -16720 q^{-10} -7209 q^{-11} +3498 q^{-12} +14845 q^{-13} +14724 q^{-14} +6619 q^{-15} -6482 q^{-16} -12944 q^{-17} -11647 q^{-18} -5804 q^{-19} +5821 q^{-20} +11713 q^{-21} +11350 q^{-22} +2872 q^{-23} -4696 q^{-24} -9434 q^{-25} -10155 q^{-26} -2946 q^{-27} +4098 q^{-28} +9167 q^{-29} +7129 q^{-30} +3105 q^{-31} -2746 q^{-32} -7734 q^{-33} -6493 q^{-34} -2737 q^{-35} +2923 q^{-36} +4996 q^{-37} +5710 q^{-38} +2795 q^{-39} -2027 q^{-40} -4233 q^{-41} -4522 q^{-42} -1751 q^{-43} +410 q^{-44} +3331 q^{-45} +3671 q^{-46} +1653 q^{-47} -388 q^{-48} -2254 q^{-49} -2234 q^{-50} -1967 q^{-51} +205 q^{-52} +1545 q^{-53} +1705 q^{-54} +1224 q^{-55} +85 q^{-56} -615 q^{-57} -1500 q^{-58} -825 q^{-59} -141 q^{-60} +428 q^{-61} +743 q^{-62} +616 q^{-63} +362 q^{-64} -403 q^{-65} -411 q^{-66} -382 q^{-67} -170 q^{-68} +64 q^{-69} +249 q^{-70} +340 q^{-71} +25 q^{-72} -16 q^{-73} -124 q^{-74} -126 q^{-75} -99 q^{-76} +6 q^{-77} +115 q^{-78} +30 q^{-79} +45 q^{-80} - q^{-81} -20 q^{-82} -48 q^{-83} -23 q^{-84} +23 q^{-85} +15 q^{-87} +7 q^{-88} +5 q^{-89} -11 q^{-90} -9 q^{-91} +5 q^{-92} -2 q^{-93} +2 q^{-94} + q^{-95} +2 q^{-96} - q^{-97} -2 q^{-98} + q^{-99} </math> |<br />
coloured_jones_7 = |<br />
computer_talk = <br />
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<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td><br />
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td><br />
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<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[6, 2, 7, 1], X[8, 4, 9, 3], X[14, 6, 15, 5], X[20, 15, 1, 16], <br />
<br />
X[16, 9, 17, 10], X[10, 19, 11, 20], X[18, 11, 19, 12], <br />
<br />
X[12, 17, 13, 18], X[2, 8, 3, 7], X[4, 14, 5, 13]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[1, -9, 2, -10, 3, -1, 9, -2, 5, -6, 7, -8, 10, -3, 4, -5, 8, <br />
<br />
-7, 6, -4]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[6, 8, 14, 2, 16, 18, 4, 20, 12, 10]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>br = BR[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[4, {1, 1, 1, -2, 1, 1, -2, -2, -3, 2, -3}]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{First[br], Crossings[br]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{4, 11}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BraidIndex[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>4</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[10, 52]]]</nowiki></code></td></tr><br />
<tr align=left><td></td><td>[[Image:10_52_ML.gif]]</td></tr><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr><br />
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> (#[Knot[10, 52]]&) /@ {<br />
SymmetryType, UnknottingNumber, ThreeGenus,<br />
BridgeIndex, SuperBridgeIndex, NakanishiIndex<br />
}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Reversible, 2, 3, 3, NotAvailable, 1}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>alex = Alexander[Knot[10, 52]][t]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 7 13 2 3<br />
-15 + -- - -- + -- + 13 t - 7 t + 2 t<br />
3 2 t<br />
t t</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[10, 52]][z]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4 6<br />
1 + 3 z + 5 z + 2 z</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 23], Knot[10, 52]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[10, 52]], KnotSignature[Knot[10, 52]]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{59, 2}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Jones[Knot[10, 52]][q]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[14]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -4 2 4 7 2 3 4 5 6<br />
-8 - q + -- - -- + - + 10 q - 9 q + 8 q - 6 q + 3 q - q<br />
3 2 q<br />
q q</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 52]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[10, 52]][q]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -12 -8 -6 2 2 6 8 10 12 14<br />
3 - q - q - q + -- + 2 q + 2 q - 2 q + q - q - q + <br />
4<br />
q<br />
<br />
16 18<br />
q - q</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[17]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>HOMFLYPT[Knot[10, 52]][a, z]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2 4 4<br />
-4 2 2 2 z 2 z 2 2 4 z 3 z<br />
4 - a - 2 a + 6 z - ---- + ---- - 3 a z + 4 z - -- + ---- - <br />
4 2 4 2<br />
a a a a<br />
<br />
6<br />
2 4 6 z<br />
a z + z + --<br />
2<br />
a</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[18]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[10, 52]][a, z]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2<br />
-4 2 2 z 7 z 3 2 6 z 4 z<br />
4 - a + 2 a + --- - --- - 9 a z - 4 a z - 9 z + ---- + ---- - <br />
5 a 4 2<br />
a a a<br />
<br />
3 3 3 3<br />
2 2 z 5 z 2 z 24 z 3 3 3 4<br />
7 a z + -- - ---- + ---- + ----- + 24 a z + 8 a z + 19 z + <br />
7 5 3 a<br />
a a a<br />
<br />
4 4 4 5 5 5<br />
3 z 12 z 9 z 2 4 6 z 11 z 28 z 5<br />
---- - ----- - ---- + 13 a z + ---- - ----- - ----- - 16 a z - <br />
6 4 2 5 3 a<br />
a a a a a<br />
<br />
6 6 7 7<br />
3 5 6 8 z 3 z 2 6 7 z 7 z 7<br />
5 a z - 20 z + ---- - ---- - 9 a z + ---- + ---- + a z + <br />
4 2 3 a<br />
a a a<br />
<br />
8 9<br />
3 7 8 4 z 2 8 z 9<br />
a z + 6 z + ---- + 2 a z + -- + a z<br />
2 a<br />
a</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[19]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[10, 52]], Vassiliev[3][Knot[10, 52]]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{3, 1}</nowiki></code></td></tr><br />
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<table><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[20]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[10, 52]][q, t]</nowiki></code></td></tr><br />
<tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[20]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 3 1 1 1 3 1 4 3<br />
6 q + 5 q + ----- + ----- + ----- + ----- + ----- + ----- + ---- + <br />
9 5 7 4 5 4 5 3 3 3 3 2 2<br />
q t q t q t q t q t q t q t<br />
<br />
4 4 q 3 5 5 2 7 2 7 3 9 3<br />
--- + --- + 4 q t + 5 q t + 4 q t + 4 q t + 2 q t + 4 q t + <br />
q t t<br />
<br />
9 4 11 4 13 5<br />
q t + 2 q t + q t</nowiki></code></td></tr><br />
</table><br />
<table><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[10, 52], 2][q]</nowiki></code></td></tr><br />
<tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -13 2 -11 7 6 9 21 6 28 37 3 52<br />
20 + q - --- - q + --- - -- - -- + -- - -- - -- + -- + -- - -- + <br />
12 10 9 8 7 6 5 4 3 2<br />
q q q q q q q q q q<br />
<br />
46 2 3 4 5 6 7 8<br />
-- - 70 q + 43 q + 35 q - 73 q + 30 q + 41 q - 60 q + 17 q + <br />
q<br />
<br />
9 10 11 12 13 14 15 16 17<br />
31 q - 37 q + 9 q + 14 q - 15 q + 4 q + 3 q - 3 q + q</nowiki></code></td></tr><br />
</table> }}</div>
DarerRacel
https://katlas.org/index.php?title=10_52&diff=1693794
10 52
2009-05-26T12:09:18Z
<p>DarerRacel: </p>
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http://www.texttrdelcali.com <br />
<!-- WARNING! WARNING! WARNING!<br />
<!-- This page was generated from the splice base [[Rolfsen_Splice_Base]]. Please do not edit!<br />
<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)<br />
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Rolfsen_Splice_Base]]. --><br />
<!-- --><br />
<!-- --><br />
{{Rolfsen Knot Page|<br />
n = 10 |<br />
k = 52 |<br />
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,2,-10,3,-1,9,-2,5,-6,7,-8,10,-3,4,-5,8,-7,6,-4/goTop.html |<br />
braid_table = <table cellspacing=0 cellpadding=0 border=0><br />
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr><br />
</table> |<br />
braid_crossings = 11 |<br />
braid_width = 4 |<br />
braid_index = 4 |<br />
same_alexander = [[10_23]], |<br />
same_jones = |<br />
khovanov_table = <table border=1><br />
<tr align=center><br />
<td width=13.3333%><table cellpadding=0 cellspacing=0><br />
<tr><td>\</td><td>&nbsp;</td><td>r</td></tr><br />
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr><br />
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr><br />
</table></td><br />
<td width=6.66667%>-5</td ><td width=6.66667%>-4</td ><td width=6.66667%>-3</td ><td width=6.66667%>-2</td ><td width=6.66667%>-1</td ><td width=6.66667%>0</td ><td width=6.66667%>1</td ><td width=6.66667%>2</td ><td width=6.66667%>3</td ><td width=6.66667%>4</td ><td width=6.66667%>5</td ><td width=13.3333%>&chi;</td></tr><br />
<tr align=center><td>13</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>-1</td></tr><br />
<tr align=center><td>11</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-3</td></tr><br />
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr><br />
<tr align=center><td>-5</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr><br />
<tr align=center><td>-7</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>-9</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
</table> |<br />
coloured_jones_2 = <math>q^{17}-3 q^{16}+3 q^{15}+4 q^{14}-15 q^{13}+14 q^{12}+9 q^{11}-37 q^{10}+31 q^9+17 q^8-60 q^7+41 q^6+30 q^5-73 q^4+35 q^3+43 q^2-70 q+20+46 q^{-1} -52 q^{-2} +3 q^{-3} +37 q^{-4} -28 q^{-5} -6 q^{-6} +21 q^{-7} -9 q^{-8} -6 q^{-9} +7 q^{-10} - q^{-11} -2 q^{-12} + q^{-13} </math> |<br />
coloured_jones_3 = <math>-q^{33}+3 q^{32}-3 q^{31}-q^{30}+3 q^{29}+4 q^{28}-9 q^{27}-4 q^{26}+19 q^{25}+2 q^{24}-35 q^{23}+5 q^{22}+53 q^{21}-9 q^{20}-85 q^{19}+20 q^{18}+117 q^{17}-22 q^{16}-156 q^{15}+18 q^{14}+190 q^{13}-6 q^{12}-210 q^{11}-24 q^{10}+228 q^9+47 q^8-216 q^7-88 q^6+211 q^5+107 q^4-173 q^3-145 q^2+155 q+150-108 q^{-1} -169 q^{-2} +80 q^{-3} +160 q^{-4} -35 q^{-5} -155 q^{-6} +6 q^{-7} +130 q^{-8} +26 q^{-9} -105 q^{-10} -43 q^{-11} +73 q^{-12} +49 q^{-13} -41 q^{-14} -48 q^{-15} +20 q^{-16} +34 q^{-17} -2 q^{-18} -24 q^{-19} -2 q^{-20} +11 q^{-21} +5 q^{-22} -6 q^{-23} -2 q^{-24} + q^{-25} +2 q^{-26} - q^{-27} </math> |<br />
coloured_jones_4 = <math>q^{54}-3 q^{53}+3 q^{52}+q^{51}-6 q^{50}+8 q^{49}-9 q^{48}+10 q^{47}-2 q^{46}-22 q^{45}+36 q^{44}-19 q^{43}+15 q^{42}-20 q^{41}-51 q^{40}+111 q^{39}-21 q^{38}-8 q^{37}-91 q^{36}-82 q^{35}+286 q^{34}+19 q^{33}-92 q^{32}-277 q^{31}-149 q^{30}+581 q^{29}+185 q^{28}-178 q^{27}-595 q^{26}-343 q^{25}+880 q^{24}+481 q^{23}-120 q^{22}-888 q^{21}-673 q^{20}+978 q^{19}+743 q^{18}+122 q^{17}-958 q^{16}-977 q^{15}+825 q^{14}+792 q^{13}+416 q^{12}-776 q^{11}-1114 q^{10}+543 q^9+643 q^8+630 q^7-478 q^6-1085 q^5+249 q^4+407 q^3+749 q^2-163 q-955-23 q^{-1} +149 q^{-2} +778 q^{-3} +137 q^{-4} -728 q^{-5} -233 q^{-6} -134 q^{-7} +672 q^{-8} +375 q^{-9} -396 q^{-10} -294 q^{-11} -378 q^{-12} +404 q^{-13} +442 q^{-14} -49 q^{-15} -163 q^{-16} -454 q^{-17} +88 q^{-18} +300 q^{-19} +141 q^{-20} +39 q^{-21} -321 q^{-22} -88 q^{-23} +84 q^{-24} +123 q^{-25} +134 q^{-26} -125 q^{-27} -83 q^{-28} -30 q^{-29} +31 q^{-30} +97 q^{-31} -17 q^{-32} -23 q^{-33} -32 q^{-34} -11 q^{-35} +35 q^{-36} +3 q^{-37} +2 q^{-38} -9 q^{-39} -9 q^{-40} +7 q^{-41} + q^{-42} +2 q^{-43} - q^{-44} -2 q^{-45} + q^{-46} </math> |<br />
coloured_jones_5 = <math>-q^{80}+3 q^{79}-3 q^{78}-q^{77}+6 q^{76}-5 q^{75}-3 q^{74}+8 q^{73}-4 q^{72}-q^{71}+8 q^{70}-12 q^{69}-11 q^{68}+21 q^{67}+14 q^{66}-5 q^{65}-22 q^{64}-34 q^{63}+7 q^{62}+75 q^{61}+66 q^{60}-59 q^{59}-162 q^{58}-103 q^{57}+133 q^{56}+334 q^{55}+192 q^{54}-276 q^{53}-619 q^{52}-366 q^{51}+470 q^{50}+1080 q^{49}+647 q^{48}-674 q^{47}-1678 q^{46}-1161 q^{45}+821 q^{44}+2461 q^{43}+1860 q^{42}-832 q^{41}-3231 q^{40}-2808 q^{39}+583 q^{38}+3964 q^{37}+3871 q^{36}-94 q^{35}-4443 q^{34}-4915 q^{33}-655 q^{32}+4597 q^{31}+5812 q^{30}+1530 q^{29}-4432 q^{28}-6383 q^{27}-2373 q^{26}+3910 q^{25}+6625 q^{24}+3128 q^{23}-3295 q^{22}-6482 q^{21}-3611 q^{20}+2501 q^{19}+6137 q^{18}+3925 q^{17}-1853 q^{16}-5565 q^{15}-3996 q^{14}+1130 q^{13}+5005 q^{12}+4030 q^{11}-634 q^{10}-4339 q^9-3928 q^8-17 q^7+3764 q^6+3906 q^5+473 q^4-3070 q^3-3745 q^2-1143 q+2397+3633 q^{-1} +1616 q^{-2} -1573 q^{-3} -3292 q^{-4} -2185 q^{-5} +740 q^{-6} +2871 q^{-7} +2475 q^{-8} +147 q^{-9} -2186 q^{-10} -2648 q^{-11} -918 q^{-12} +1415 q^{-13} +2448 q^{-14} +1536 q^{-15} -529 q^{-16} -2055 q^{-17} -1844 q^{-18} -246 q^{-19} +1386 q^{-20} +1846 q^{-21} +874 q^{-22} -681 q^{-23} -1559 q^{-24} -1177 q^{-25} +13 q^{-26} +1052 q^{-27} +1218 q^{-28} +471 q^{-29} -529 q^{-30} -995 q^{-31} -681 q^{-32} +44 q^{-33} +644 q^{-34} +702 q^{-35} +239 q^{-36} -302 q^{-37} -520 q^{-38} -362 q^{-39} +21 q^{-40} +326 q^{-41} +328 q^{-42} +110 q^{-43} -121 q^{-44} -234 q^{-45} -155 q^{-46} +16 q^{-47} +120 q^{-48} +120 q^{-49} +50 q^{-50} -50 q^{-51} -81 q^{-52} -39 q^{-53} +2 q^{-54} +32 q^{-55} +40 q^{-56} +8 q^{-57} -19 q^{-58} -13 q^{-59} -8 q^{-60} -2 q^{-61} +11 q^{-62} +7 q^{-63} -3 q^{-64} -2 q^{-65} - q^{-66} -2 q^{-67} + q^{-68} +2 q^{-69} - q^{-70} </math> |<br />
coloured_jones_6 = <math>q^{111}-3 q^{110}+3 q^{109}+q^{108}-6 q^{107}+5 q^{106}+4 q^{104}-14 q^{103}+7 q^{102}+15 q^{101}-26 q^{100}+18 q^{99}+5 q^{98}-5 q^{97}-37 q^{96}+22 q^{95}+59 q^{94}-62 q^{93}+23 q^{92}-6 q^{91}-42 q^{90}-55 q^{89}+123 q^{88}+192 q^{87}-164 q^{86}-100 q^{85}-170 q^{84}-129 q^{83}+115 q^{82}+596 q^{81}+612 q^{80}-468 q^{79}-798 q^{78}-963 q^{77}-422 q^{76}+901 q^{75}+2241 q^{74}+1962 q^{73}-996 q^{72}-2896 q^{71}-3549 q^{70}-1659 q^{69}+2553 q^{68}+6269 q^{67}+5743 q^{66}-877 q^{65}-6779 q^{64}-9469 q^{63}-5700 q^{62}+3925 q^{61}+12961 q^{60}+13693 q^{59}+2283 q^{58}-10692 q^{57}-18675 q^{56}-14467 q^{55}+1913 q^{54}+19644 q^{53}+25210 q^{52}+10645 q^{51}-10654 q^{50}-27467 q^{49}-26739 q^{48}-5805 q^{47}+21506 q^{46}+35577 q^{45}+22409 q^{44}-4323 q^{43}-30514 q^{42}-37060 q^{41}-16824 q^{40}+16488 q^{39}+39319 q^{38}+31754 q^{37}+5350 q^{36}-26325 q^{35}-40357 q^{34}-25325 q^{33}+8043 q^{32}+35758 q^{31}+34436 q^{30}+12861 q^{29}-18752 q^{28}-36938 q^{27}-28088 q^{26}+1142 q^{25}+29006 q^{24}+31710 q^{23}+16027 q^{22}-12149 q^{21}-31018 q^{20}-27007 q^{19}-2896 q^{18}+22750 q^{17}+27575 q^{16}+16999 q^{15}-7174 q^{14}-25518 q^{13}-25488 q^{12}-6194 q^{11}+17092 q^{10}+24019 q^9+18392 q^8-1873 q^7-19974 q^6-24460 q^5-10547 q^4+10191 q^3+19883 q^2+20150 q+4894-12517 q^{-1} -22066 q^{-2} -15065 q^{-3} +1389 q^{-4} +13095 q^{-5} +19786 q^{-6} +11592 q^{-7} -2785 q^{-8} -16031 q^{-9} -16720 q^{-10} -7209 q^{-11} +3498 q^{-12} +14845 q^{-13} +14724 q^{-14} +6619 q^{-15} -6482 q^{-16} -12944 q^{-17} -11647 q^{-18} -5804 q^{-19} +5821 q^{-20} +11713 q^{-21} +11350 q^{-22} +2872 q^{-23} -4696 q^{-24} -9434 q^{-25} -10155 q^{-26} -2946 q^{-27} +4098 q^{-28} +9167 q^{-29} +7129 q^{-30} +3105 q^{-31} -2746 q^{-32} -7734 q^{-33} -6493 q^{-34} -2737 q^{-35} +2923 q^{-36} +4996 q^{-37} +5710 q^{-38} +2795 q^{-39} -2027 q^{-40} -4233 q^{-41} -4522 q^{-42} -1751 q^{-43} +410 q^{-44} +3331 q^{-45} +3671 q^{-46} +1653 q^{-47} -388 q^{-48} -2254 q^{-49} -2234 q^{-50} -1967 q^{-51} +205 q^{-52} +1545 q^{-53} +1705 q^{-54} +1224 q^{-55} +85 q^{-56} -615 q^{-57} -1500 q^{-58} -825 q^{-59} -141 q^{-60} +428 q^{-61} +743 q^{-62} +616 q^{-63} +362 q^{-64} -403 q^{-65} -411 q^{-66} -382 q^{-67} -170 q^{-68} +64 q^{-69} +249 q^{-70} +340 q^{-71} +25 q^{-72} -16 q^{-73} -124 q^{-74} -126 q^{-75} -99 q^{-76} +6 q^{-77} +115 q^{-78} +30 q^{-79} +45 q^{-80} - q^{-81} -20 q^{-82} -48 q^{-83} -23 q^{-84} +23 q^{-85} +15 q^{-87} +7 q^{-88} +5 q^{-89} -11 q^{-90} -9 q^{-91} +5 q^{-92} -2 q^{-93} +2 q^{-94} + q^{-95} +2 q^{-96} - q^{-97} -2 q^{-98} + q^{-99} </math> |<br />
coloured_jones_7 = |<br />
computer_talk = <br />
<table><br />
<tr valign=top><br />
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td><br />
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td><br />
</tr><br />
<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[6, 2, 7, 1], X[8, 4, 9, 3], X[14, 6, 15, 5], X[20, 15, 1, 16], <br />
<br />
X[16, 9, 17, 10], X[10, 19, 11, 20], X[18, 11, 19, 12], <br />
<br />
X[12, 17, 13, 18], X[2, 8, 3, 7], X[4, 14, 5, 13]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[1, -9, 2, -10, 3, -1, 9, -2, 5, -6, 7, -8, 10, -3, 4, -5, 8, <br />
<br />
-7, 6, -4]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[6, 8, 14, 2, 16, 18, 4, 20, 12, 10]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>br = BR[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[4, {1, 1, 1, -2, 1, 1, -2, -2, -3, 2, -3}]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{First[br], Crossings[br]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{4, 11}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BraidIndex[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>4</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[10, 52]]]</nowiki></code></td></tr><br />
<tr align=left><td></td><td>[[Image:10_52_ML.gif]]</td></tr><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> (#[Knot[10, 52]]&) /@ {<br />
SymmetryType, UnknottingNumber, ThreeGenus,<br />
BridgeIndex, SuperBridgeIndex, NakanishiIndex<br />
}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Reversible, 2, 3, 3, NotAvailable, 1}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>alex = Alexander[Knot[10, 52]][t]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 7 13 2 3<br />
-15 + -- - -- + -- + 13 t - 7 t + 2 t<br />
3 2 t<br />
t t</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[10, 52]][z]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4 6<br />
1 + 3 z + 5 z + 2 z</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 23], Knot[10, 52]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[10, 52]], KnotSignature[Knot[10, 52]]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{59, 2}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Jones[Knot[10, 52]][q]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[14]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -4 2 4 7 2 3 4 5 6<br />
-8 - q + -- - -- + - + 10 q - 9 q + 8 q - 6 q + 3 q - q<br />
3 2 q<br />
q q</nowiki></code></td></tr><br />
</table><br />
<table><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 52]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[10, 52]][q]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -12 -8 -6 2 2 6 8 10 12 14<br />
3 - q - q - q + -- + 2 q + 2 q - 2 q + q - q - q + <br />
4<br />
q<br />
<br />
16 18<br />
q - q</nowiki></code></td></tr><br />
</table><br />
<table><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[17]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>HOMFLYPT[Knot[10, 52]][a, z]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2 4 4<br />
-4 2 2 2 z 2 z 2 2 4 z 3 z<br />
4 - a - 2 a + 6 z - ---- + ---- - 3 a z + 4 z - -- + ---- - <br />
4 2 4 2<br />
a a a a<br />
<br />
6<br />
2 4 6 z<br />
a z + z + --<br />
2<br />
a</nowiki></code></td></tr><br />
</table><br />
<table><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[18]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[10, 52]][a, z]</nowiki></code></td></tr><br />
<tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2<br />
-4 2 2 z 7 z 3 2 6 z 4 z<br />
4 - a + 2 a + --- - --- - 9 a z - 4 a z - 9 z + ---- + ---- - <br />
5 a 4 2<br />
a a a<br />
<br />
3 3 3 3<br />
2 2 z 5 z 2 z 24 z 3 3 3 4<br />
7 a z + -- - ---- + ---- + ----- + 24 a z + 8 a z + 19 z + <br />
7 5 3 a<br />
a a a<br />
<br />
4 4 4 5 5 5<br />
3 z 12 z 9 z 2 4 6 z 11 z 28 z 5<br />
---- - ----- - ---- + 13 a z + ---- - ----- - ----- - 16 a z - <br />
6 4 2 5 3 a<br />
a a a a a<br />
<br />
6 6 7 7<br />
3 5 6 8 z 3 z 2 6 7 z 7 z 7<br />
5 a z - 20 z + ---- - ---- - 9 a z + ---- + ---- + a z + <br />
4 2 3 a<br />
a a a<br />
<br />
8 9<br />
3 7 8 4 z 2 8 z 9<br />
a z + 6 z + ---- + 2 a z + -- + a z<br />
2 a<br />
a</nowiki></code></td></tr><br />
</table><br />
<table><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[19]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[10, 52]], Vassiliev[3][Knot[10, 52]]}</nowiki></code></td></tr><br />
<tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{3, 1}</nowiki></code></td></tr><br />
</table><br />
<table><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[20]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[10, 52]][q, t]</nowiki></code></td></tr><br />
<tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[20]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 3 1 1 1 3 1 4 3<br />
6 q + 5 q + ----- + ----- + ----- + ----- + ----- + ----- + ---- + <br />
9 5 7 4 5 4 5 3 3 3 3 2 2<br />
q t q t q t q t q t q t q t<br />
<br />
4 4 q 3 5 5 2 7 2 7 3 9 3<br />
--- + --- + 4 q t + 5 q t + 4 q t + 4 q t + 2 q t + 4 q t + <br />
q t t<br />
<br />
9 4 11 4 13 5<br />
q t + 2 q t + q t</nowiki></code></td></tr><br />
</table><br />
<table><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[10, 52], 2][q]</nowiki></code></td></tr><br />
<tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -13 2 -11 7 6 9 21 6 28 37 3 52<br />
20 + q - --- - q + --- - -- - -- + -- - -- - -- + -- + -- - -- + <br />
12 10 9 8 7 6 5 4 3 2<br />
q q q q q q q q q q<br />
<br />
46 2 3 4 5 6 7 8<br />
-- - 70 q + 43 q + 35 q - 73 q + 30 q + 41 q - 60 q + 17 q + <br />
q<br />
<br />
9 10 11 12 13 14 15 16 17<br />
31 q - 37 q + 9 q + 14 q - 15 q + 4 q + 3 q - 3 q + q</nowiki></code></td></tr><br />
</table> }}</div>
DarerRacel
https://katlas.org/index.php?title=10_52&diff=1693756
10 52
2009-05-22T17:29:05Z
<p>DarerRacel: </p>
<hr />
<div>http://www.texttrdelcali.com <br />
<!-- WARNING! WARNING! WARNING!<br />
<!-- This page was generated from the splice base [[Rolfsen_Splice_Base]]. Please do not edit!<br />
<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)<br />
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Rolfsen_Splice_Base]]. --><br />
<!-- --><br />
<!-- --><br />
{{Rolfsen Knot Page|<br />
n = 10 |<br />
k = 52 |<br />
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,2,-10,3,-1,9,-2,5,-6,7,-8,10,-3,4,-5,8,-7,6,-4/goTop.html |<br />
braid_table = <table cellspacing=0 cellpadding=0 border=0><br />
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr><br />
</table> |<br />
braid_crossings = 11 |<br />
braid_width = 4 |<br />
braid_index = 4 |<br />
same_alexander = [[10_23]], |<br />
same_jones = |<br />
khovanov_table = <table border=1><br />
<tr align=center><br />
<td width=13.3333%><table cellpadding=0 cellspacing=0><br />
<tr><td>\</td><td>&nbsp;</td><td>r</td></tr><br />
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr><br />
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr><br />
</table></td><br />
<td width=6.66667%>-5</td ><td width=6.66667%>-4</td ><td width=6.66667%>-3</td ><td width=6.66667%>-2</td ><td width=6.66667%>-1</td ><td width=6.66667%>0</td ><td width=6.66667%>1</td ><td width=6.66667%>2</td ><td width=6.66667%>3</td ><td width=6.66667%>4</td ><td width=6.66667%>5</td ><td width=13.3333%>&chi;</td></tr><br />
<tr align=center><td>13</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>-1</td></tr><br />
<tr align=center><td>11</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-3</td></tr><br />
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr><br />
<tr align=center><td>-5</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr><br />
<tr align=center><td>-7</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>-9</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
</table> |<br />
coloured_jones_2 = <math>q^{17}-3 q^{16}+3 q^{15}+4 q^{14}-15 q^{13}+14 q^{12}+9 q^{11}-37 q^{10}+31 q^9+17 q^8-60 q^7+41 q^6+30 q^5-73 q^4+35 q^3+43 q^2-70 q+20+46 q^{-1} -52 q^{-2} +3 q^{-3} +37 q^{-4} -28 q^{-5} -6 q^{-6} +21 q^{-7} -9 q^{-8} -6 q^{-9} +7 q^{-10} - q^{-11} -2 q^{-12} + q^{-13} </math> |<br />
coloured_jones_3 = <math>-q^{33}+3 q^{32}-3 q^{31}-q^{30}+3 q^{29}+4 q^{28}-9 q^{27}-4 q^{26}+19 q^{25}+2 q^{24}-35 q^{23}+5 q^{22}+53 q^{21}-9 q^{20}-85 q^{19}+20 q^{18}+117 q^{17}-22 q^{16}-156 q^{15}+18 q^{14}+190 q^{13}-6 q^{12}-210 q^{11}-24 q^{10}+228 q^9+47 q^8-216 q^7-88 q^6+211 q^5+107 q^4-173 q^3-145 q^2+155 q+150-108 q^{-1} -169 q^{-2} +80 q^{-3} +160 q^{-4} -35 q^{-5} -155 q^{-6} +6 q^{-7} +130 q^{-8} +26 q^{-9} -105 q^{-10} -43 q^{-11} +73 q^{-12} +49 q^{-13} -41 q^{-14} -48 q^{-15} +20 q^{-16} +34 q^{-17} -2 q^{-18} -24 q^{-19} -2 q^{-20} +11 q^{-21} +5 q^{-22} -6 q^{-23} -2 q^{-24} + q^{-25} +2 q^{-26} - q^{-27} </math> |<br />
coloured_jones_4 = <math>q^{54}-3 q^{53}+3 q^{52}+q^{51}-6 q^{50}+8 q^{49}-9 q^{48}+10 q^{47}-2 q^{46}-22 q^{45}+36 q^{44}-19 q^{43}+15 q^{42}-20 q^{41}-51 q^{40}+111 q^{39}-21 q^{38}-8 q^{37}-91 q^{36}-82 q^{35}+286 q^{34}+19 q^{33}-92 q^{32}-277 q^{31}-149 q^{30}+581 q^{29}+185 q^{28}-178 q^{27}-595 q^{26}-343 q^{25}+880 q^{24}+481 q^{23}-120 q^{22}-888 q^{21}-673 q^{20}+978 q^{19}+743 q^{18}+122 q^{17}-958 q^{16}-977 q^{15}+825 q^{14}+792 q^{13}+416 q^{12}-776 q^{11}-1114 q^{10}+543 q^9+643 q^8+630 q^7-478 q^6-1085 q^5+249 q^4+407 q^3+749 q^2-163 q-955-23 q^{-1} +149 q^{-2} +778 q^{-3} +137 q^{-4} -728 q^{-5} -233 q^{-6} -134 q^{-7} +672 q^{-8} +375 q^{-9} -396 q^{-10} -294 q^{-11} -378 q^{-12} +404 q^{-13} +442 q^{-14} -49 q^{-15} -163 q^{-16} -454 q^{-17} +88 q^{-18} +300 q^{-19} +141 q^{-20} +39 q^{-21} -321 q^{-22} -88 q^{-23} +84 q^{-24} +123 q^{-25} +134 q^{-26} -125 q^{-27} -83 q^{-28} -30 q^{-29} +31 q^{-30} +97 q^{-31} -17 q^{-32} -23 q^{-33} -32 q^{-34} -11 q^{-35} +35 q^{-36} +3 q^{-37} +2 q^{-38} -9 q^{-39} -9 q^{-40} +7 q^{-41} + q^{-42} +2 q^{-43} - q^{-44} -2 q^{-45} + q^{-46} </math> |<br />
coloured_jones_5 = <math>-q^{80}+3 q^{79}-3 q^{78}-q^{77}+6 q^{76}-5 q^{75}-3 q^{74}+8 q^{73}-4 q^{72}-q^{71}+8 q^{70}-12 q^{69}-11 q^{68}+21 q^{67}+14 q^{66}-5 q^{65}-22 q^{64}-34 q^{63}+7 q^{62}+75 q^{61}+66 q^{60}-59 q^{59}-162 q^{58}-103 q^{57}+133 q^{56}+334 q^{55}+192 q^{54}-276 q^{53}-619 q^{52}-366 q^{51}+470 q^{50}+1080 q^{49}+647 q^{48}-674 q^{47}-1678 q^{46}-1161 q^{45}+821 q^{44}+2461 q^{43}+1860 q^{42}-832 q^{41}-3231 q^{40}-2808 q^{39}+583 q^{38}+3964 q^{37}+3871 q^{36}-94 q^{35}-4443 q^{34}-4915 q^{33}-655 q^{32}+4597 q^{31}+5812 q^{30}+1530 q^{29}-4432 q^{28}-6383 q^{27}-2373 q^{26}+3910 q^{25}+6625 q^{24}+3128 q^{23}-3295 q^{22}-6482 q^{21}-3611 q^{20}+2501 q^{19}+6137 q^{18}+3925 q^{17}-1853 q^{16}-5565 q^{15}-3996 q^{14}+1130 q^{13}+5005 q^{12}+4030 q^{11}-634 q^{10}-4339 q^9-3928 q^8-17 q^7+3764 q^6+3906 q^5+473 q^4-3070 q^3-3745 q^2-1143 q+2397+3633 q^{-1} +1616 q^{-2} -1573 q^{-3} -3292 q^{-4} -2185 q^{-5} +740 q^{-6} +2871 q^{-7} +2475 q^{-8} +147 q^{-9} -2186 q^{-10} -2648 q^{-11} -918 q^{-12} +1415 q^{-13} +2448 q^{-14} +1536 q^{-15} -529 q^{-16} -2055 q^{-17} -1844 q^{-18} -246 q^{-19} +1386 q^{-20} +1846 q^{-21} +874 q^{-22} -681 q^{-23} -1559 q^{-24} -1177 q^{-25} +13 q^{-26} +1052 q^{-27} +1218 q^{-28} +471 q^{-29} -529 q^{-30} -995 q^{-31} -681 q^{-32} +44 q^{-33} +644 q^{-34} +702 q^{-35} +239 q^{-36} -302 q^{-37} -520 q^{-38} -362 q^{-39} +21 q^{-40} +326 q^{-41} +328 q^{-42} +110 q^{-43} -121 q^{-44} -234 q^{-45} -155 q^{-46} +16 q^{-47} +120 q^{-48} +120 q^{-49} +50 q^{-50} -50 q^{-51} -81 q^{-52} -39 q^{-53} +2 q^{-54} +32 q^{-55} +40 q^{-56} +8 q^{-57} -19 q^{-58} -13 q^{-59} -8 q^{-60} -2 q^{-61} +11 q^{-62} +7 q^{-63} -3 q^{-64} -2 q^{-65} - q^{-66} -2 q^{-67} + q^{-68} +2 q^{-69} - q^{-70} </math> |<br />
coloured_jones_6 = <math>q^{111}-3 q^{110}+3 q^{109}+q^{108}-6 q^{107}+5 q^{106}+4 q^{104}-14 q^{103}+7 q^{102}+15 q^{101}-26 q^{100}+18 q^{99}+5 q^{98}-5 q^{97}-37 q^{96}+22 q^{95}+59 q^{94}-62 q^{93}+23 q^{92}-6 q^{91}-42 q^{90}-55 q^{89}+123 q^{88}+192 q^{87}-164 q^{86}-100 q^{85}-170 q^{84}-129 q^{83}+115 q^{82}+596 q^{81}+612 q^{80}-468 q^{79}-798 q^{78}-963 q^{77}-422 q^{76}+901 q^{75}+2241 q^{74}+1962 q^{73}-996 q^{72}-2896 q^{71}-3549 q^{70}-1659 q^{69}+2553 q^{68}+6269 q^{67}+5743 q^{66}-877 q^{65}-6779 q^{64}-9469 q^{63}-5700 q^{62}+3925 q^{61}+12961 q^{60}+13693 q^{59}+2283 q^{58}-10692 q^{57}-18675 q^{56}-14467 q^{55}+1913 q^{54}+19644 q^{53}+25210 q^{52}+10645 q^{51}-10654 q^{50}-27467 q^{49}-26739 q^{48}-5805 q^{47}+21506 q^{46}+35577 q^{45}+22409 q^{44}-4323 q^{43}-30514 q^{42}-37060 q^{41}-16824 q^{40}+16488 q^{39}+39319 q^{38}+31754 q^{37}+5350 q^{36}-26325 q^{35}-40357 q^{34}-25325 q^{33}+8043 q^{32}+35758 q^{31}+34436 q^{30}+12861 q^{29}-18752 q^{28}-36938 q^{27}-28088 q^{26}+1142 q^{25}+29006 q^{24}+31710 q^{23}+16027 q^{22}-12149 q^{21}-31018 q^{20}-27007 q^{19}-2896 q^{18}+22750 q^{17}+27575 q^{16}+16999 q^{15}-7174 q^{14}-25518 q^{13}-25488 q^{12}-6194 q^{11}+17092 q^{10}+24019 q^9+18392 q^8-1873 q^7-19974 q^6-24460 q^5-10547 q^4+10191 q^3+19883 q^2+20150 q+4894-12517 q^{-1} -22066 q^{-2} -15065 q^{-3} +1389 q^{-4} +13095 q^{-5} +19786 q^{-6} +11592 q^{-7} -2785 q^{-8} -16031 q^{-9} -16720 q^{-10} -7209 q^{-11} +3498 q^{-12} +14845 q^{-13} +14724 q^{-14} +6619 q^{-15} -6482 q^{-16} -12944 q^{-17} -11647 q^{-18} -5804 q^{-19} +5821 q^{-20} +11713 q^{-21} +11350 q^{-22} +2872 q^{-23} -4696 q^{-24} -9434 q^{-25} -10155 q^{-26} -2946 q^{-27} +4098 q^{-28} +9167 q^{-29} +7129 q^{-30} +3105 q^{-31} -2746 q^{-32} -7734 q^{-33} -6493 q^{-34} -2737 q^{-35} +2923 q^{-36} +4996 q^{-37} +5710 q^{-38} +2795 q^{-39} -2027 q^{-40} -4233 q^{-41} -4522 q^{-42} -1751 q^{-43} +410 q^{-44} +3331 q^{-45} +3671 q^{-46} +1653 q^{-47} -388 q^{-48} -2254 q^{-49} -2234 q^{-50} -1967 q^{-51} +205 q^{-52} +1545 q^{-53} +1705 q^{-54} +1224 q^{-55} +85 q^{-56} -615 q^{-57} -1500 q^{-58} -825 q^{-59} -141 q^{-60} +428 q^{-61} +743 q^{-62} +616 q^{-63} +362 q^{-64} -403 q^{-65} -411 q^{-66} -382 q^{-67} -170 q^{-68} +64 q^{-69} +249 q^{-70} +340 q^{-71} +25 q^{-72} -16 q^{-73} -124 q^{-74} -126 q^{-75} -99 q^{-76} +6 q^{-77} +115 q^{-78} +30 q^{-79} +45 q^{-80} - q^{-81} -20 q^{-82} -48 q^{-83} -23 q^{-84} +23 q^{-85} +15 q^{-87} +7 q^{-88} +5 q^{-89} -11 q^{-90} -9 q^{-91} +5 q^{-92} -2 q^{-93} +2 q^{-94} + q^{-95} +2 q^{-96} - q^{-97} -2 q^{-98} + q^{-99} </math> |<br />
coloured_jones_7 = |<br />
computer_talk = <br />
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<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td><br />
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td><br />
</tr><br />
<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[6, 2, 7, 1], X[8, 4, 9, 3], X[14, 6, 15, 5], X[20, 15, 1, 16], <br />
<br />
X[16, 9, 17, 10], X[10, 19, 11, 20], X[18, 11, 19, 12], <br />
<br />
X[12, 17, 13, 18], X[2, 8, 3, 7], X[4, 14, 5, 13]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[1, -9, 2, -10, 3, -1, 9, -2, 5, -6, 7, -8, 10, -3, 4, -5, 8, <br />
<br />
-7, 6, -4]</nowiki></code></td></tr><br />
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<table><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[6, 8, 14, 2, 16, 18, 4, 20, 12, 10]</nowiki></code></td></tr><br />
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<table><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>br = BR[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[4, {1, 1, 1, -2, 1, 1, -2, -2, -3, 2, -3}]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{First[br], Crossings[br]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{4, 11}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BraidIndex[Knot[10, 52]]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>4</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[10, 52]]]</nowiki></code></td></tr><br />
<tr align=left><td></td><td>[[Image:10_52_ML.gif]]</td></tr><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> (#[Knot[10, 52]]&) /@ {<br />
SymmetryType, UnknottingNumber, ThreeGenus,<br />
BridgeIndex, SuperBridgeIndex, NakanishiIndex<br />
}</nowiki></code></td></tr><br />
<tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Reversible, 2, 3, 3, NotAvailable, 1}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>alex = Alexander[Knot[10, 52]][t]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 7 13 2 3<br />
-15 + -- - -- + -- + 13 t - 7 t + 2 t<br />
3 2 t<br />
t t</nowiki></code></td></tr><br />
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<table><tr align=left><br />
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[10, 52]][z]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4 6<br />
1 + 3 z + 5 z + 2 z</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 23], Knot[10, 52]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[10, 52]], KnotSignature[Knot[10, 52]]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{59, 2}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Jones[Knot[10, 52]][q]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[14]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -4 2 4 7 2 3 4 5 6<br />
-8 - q + -- - -- + - + 10 q - 9 q + 8 q - 6 q + 3 q - q<br />
3 2 q<br />
q q</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 52]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[10, 52]][q]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -12 -8 -6 2 2 6 8 10 12 14<br />
3 - q - q - q + -- + 2 q + 2 q - 2 q + q - q - q + <br />
4<br />
q<br />
<br />
16 18<br />
q - q</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[17]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>HOMFLYPT[Knot[10, 52]][a, z]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2 4 4<br />
-4 2 2 2 z 2 z 2 2 4 z 3 z<br />
4 - a - 2 a + 6 z - ---- + ---- - 3 a z + 4 z - -- + ---- - <br />
4 2 4 2<br />
a a a a<br />
<br />
6<br />
2 4 6 z<br />
a z + z + --<br />
2<br />
a</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[18]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[10, 52]][a, z]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2<br />
-4 2 2 z 7 z 3 2 6 z 4 z<br />
4 - a + 2 a + --- - --- - 9 a z - 4 a z - 9 z + ---- + ---- - <br />
5 a 4 2<br />
a a a<br />
<br />
3 3 3 3<br />
2 2 z 5 z 2 z 24 z 3 3 3 4<br />
7 a z + -- - ---- + ---- + ----- + 24 a z + 8 a z + 19 z + <br />
7 5 3 a<br />
a a a<br />
<br />
4 4 4 5 5 5<br />
3 z 12 z 9 z 2 4 6 z 11 z 28 z 5<br />
---- - ----- - ---- + 13 a z + ---- - ----- - ----- - 16 a z - <br />
6 4 2 5 3 a<br />
a a a a a<br />
<br />
6 6 7 7<br />
3 5 6 8 z 3 z 2 6 7 z 7 z 7<br />
5 a z - 20 z + ---- - ---- - 9 a z + ---- + ---- + a z + <br />
4 2 3 a<br />
a a a<br />
<br />
8 9<br />
3 7 8 4 z 2 8 z 9<br />
a z + 6 z + ---- + 2 a z + -- + a z<br />
2 a<br />
a</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[19]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[10, 52]], Vassiliev[3][Knot[10, 52]]}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{3, 1}</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[20]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[10, 52]][q, t]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[20]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 3 1 1 1 3 1 4 3<br />
6 q + 5 q + ----- + ----- + ----- + ----- + ----- + ----- + ---- + <br />
9 5 7 4 5 4 5 3 3 3 3 2 2<br />
q t q t q t q t q t q t q t<br />
<br />
4 4 q 3 5 5 2 7 2 7 3 9 3<br />
--- + --- + 4 q t + 5 q t + 4 q t + 4 q t + 2 q t + 4 q t + <br />
q t t<br />
<br />
9 4 11 4 13 5<br />
q t + 2 q t + q t</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td><br />
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[10, 52], 2][q]</nowiki></code></td></tr><br />
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td><br />
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -13 2 -11 7 6 9 21 6 28 37 3 52<br />
20 + q - --- - q + --- - -- - -- + -- - -- - -- + -- + -- - -- + <br />
12 10 9 8 7 6 5 4 3 2<br />
q q q q q q q q q q<br />
<br />
46 2 3 4 5 6 7 8<br />
-- - 70 q + 43 q + 35 q - 73 q + 30 q + 41 q - 60 q + 17 q + <br />
q<br />
<br />
9 10 11 12 13 14 15 16 17<br />
31 q - 37 q + 9 q + 14 q - 15 q + 4 q + 3 q - 3 q + q</nowiki></code></td></tr><br />
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DarerRacel