8 18

2008-12-17T06:17:19Z

LinoeRtasi: bolierbasc

baselacel



{{Rolfsen Knot Page|
n = 8 |
k = 18 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,2,-5,6,-1,7,-2,8,-6,3,-7,4,-8,5,-3/goTop.html |
braid_table = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]</td></tr>
</table> |
braid_crossings = 8 |
braid_width = 3 |
braid_index = 3 |
same_alexander = [[9_24]], [[K11n85]], [[K11n164]], |
same_jones = |
khovanov_table = <table border=1>
<tr align=center>
<td width=15.3846%><table cellpadding=0 cellspacing=0>
<tr><td>\</td><td> </td><td>r</td></tr>
<tr><td> </td><td> \ </td><td> </td></tr>
<tr><td>j</td><td> </td><td>\</td></tr>
</table></td>
<td width=7.69231%>-4</td ><td width=7.69231%>-3</td ><td width=7.69231%>-2</td ><td width=7.69231%>-1</td ><td width=7.69231%>0</td ><td width=7.69231%>1</td ><td width=7.69231%>2</td ><td width=7.69231%>3</td ><td width=7.69231%>4</td ><td width=15.3846%>χ</td></tr>
<tr align=center><td>9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>1</td><td>1</td></tr>
<tr align=center><td>7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow> </td><td>-3</td></tr>
<tr align=center><td>5</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td> </td><td>2</td></tr>
<tr align=center><td>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>4</td><td bgcolor=yellow>3</td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>1</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>5</td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td>2</td></tr>
<tr align=center><td>-1</td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>5</td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr>
<tr align=center><td>-3</td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>4</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>-5</td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr>
<tr align=center><td>-7</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-3</td></tr>
<tr align=center><td>-9</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
</table> |
coloured_jones_2 = <math>q^{12}-4 q^{11}+2 q^{10}+13 q^9-21 q^8-4 q^7+41 q^6-38 q^5-20 q^4+69 q^3-43 q^2-36 q+81-36 q^{-1} -43 q^{-2} +69 q^{-3} -20 q^{-4} -38 q^{-5} +41 q^{-6} -4 q^{-7} -21 q^{-8} +13 q^{-9} +2 q^{-10} -4 q^{-11} + q^{-12} </math> |
coloured_jones_3 = <math>q^{24}-4 q^{23}+2 q^{22}+9 q^{21}-q^{20}-24 q^{19}-10 q^{18}+55 q^{17}+27 q^{16}-79 q^{15}-73 q^{14}+108 q^{13}+130 q^{12}-121 q^{11}-199 q^{10}+119 q^9+266 q^8-105 q^7-322 q^6+74 q^5+374 q^4-53 q^3-389 q^2+10 q+411+10 q^{-1} -389 q^{-2} -53 q^{-3} +374 q^{-4} +74 q^{-5} -322 q^{-6} -105 q^{-7} +266 q^{-8} +119 q^{-9} -199 q^{-10} -121 q^{-11} +130 q^{-12} +108 q^{-13} -73 q^{-14} -79 q^{-15} +27 q^{-16} +55 q^{-17} -10 q^{-18} -24 q^{-19} - q^{-20} +9 q^{-21} +2 q^{-22} -4 q^{-23} + q^{-24} </math> |
coloured_jones_4 = <math>q^{40}-4 q^{39}+2 q^{38}+9 q^{37}-5 q^{36}-4 q^{35}-30 q^{34}+14 q^{33}+66 q^{32}+10 q^{31}-20 q^{30}-173 q^{29}-36 q^{28}+217 q^{27}+184 q^{26}+77 q^{25}-483 q^{24}-344 q^{23}+280 q^{22}+558 q^{21}+530 q^{20}-729 q^{19}-930 q^{18}-11 q^{17}+880 q^{16}+1297 q^{15}-647 q^{14}-1490 q^{13}-605 q^{12}+916 q^{11}+2042 q^{10}-297 q^9-1774 q^8-1196 q^7+714 q^6+2508 q^5+97 q^4-1785 q^3-1595 q^2+427 q+2659+427 q^{-1} -1595 q^{-2} -1785 q^{-3} +97 q^{-4} +2508 q^{-5} +714 q^{-6} -1196 q^{-7} -1774 q^{-8} -297 q^{-9} +2042 q^{-10} +916 q^{-11} -605 q^{-12} -1490 q^{-13} -647 q^{-14} +1297 q^{-15} +880 q^{-16} -11 q^{-17} -930 q^{-18} -729 q^{-19} +530 q^{-20} +558 q^{-21} +280 q^{-22} -344 q^{-23} -483 q^{-24} +77 q^{-25} +184 q^{-26} +217 q^{-27} -36 q^{-28} -173 q^{-29} -20 q^{-30} +10 q^{-31} +66 q^{-32} +14 q^{-33} -30 q^{-34} -4 q^{-35} -5 q^{-36} +9 q^{-37} +2 q^{-38} -4 q^{-39} + q^{-40} </math> |
coloured_jones_5 = <math>q^{60}-4 q^{59}+2 q^{58}+9 q^{57}-5 q^{56}-8 q^{55}-10 q^{54}-6 q^{53}+25 q^{52}+59 q^{51}+15 q^{50}-78 q^{49}-132 q^{48}-88 q^{47}+108 q^{46}+310 q^{45}+309 q^{44}-82 q^{43}-588 q^{42}-694 q^{41}-160 q^{40}+793 q^{39}+1380 q^{38}+769 q^{37}-888 q^{36}-2171 q^{35}-1762 q^{34}+471 q^{33}+2960 q^{32}+3222 q^{31}+409 q^{30}-3440 q^{29}-4844 q^{28}-1921 q^{27}+3420 q^{26}+6480 q^{25}+3843 q^{24}-2833 q^{23}-7798 q^{22}-5983 q^{21}+1728 q^{20}+8665 q^{19}+8083 q^{18}-291 q^{17}-9075 q^{16}-9861 q^{15}-1314 q^{14}+9043 q^{13}+11334 q^{12}+2801 q^{11}-8752 q^{10}-12285 q^9-4191 q^8+8219 q^7+13045 q^6+5245 q^5-7664 q^4-13289 q^3-6232 q^2+6937 q+13529+6937 q^{-1} -6232 q^{-2} -13289 q^{-3} -7664 q^{-4} +5245 q^{-5} +13045 q^{-6} +8219 q^{-7} -4191 q^{-8} -12285 q^{-9} -8752 q^{-10} +2801 q^{-11} +11334 q^{-12} +9043 q^{-13} -1314 q^{-14} -9861 q^{-15} -9075 q^{-16} -291 q^{-17} +8083 q^{-18} +8665 q^{-19} +1728 q^{-20} -5983 q^{-21} -7798 q^{-22} -2833 q^{-23} +3843 q^{-24} +6480 q^{-25} +3420 q^{-26} -1921 q^{-27} -4844 q^{-28} -3440 q^{-29} +409 q^{-30} +3222 q^{-31} +2960 q^{-32} +471 q^{-33} -1762 q^{-34} -2171 q^{-35} -888 q^{-36} +769 q^{-37} +1380 q^{-38} +793 q^{-39} -160 q^{-40} -694 q^{-41} -588 q^{-42} -82 q^{-43} +309 q^{-44} +310 q^{-45} +108 q^{-46} -88 q^{-47} -132 q^{-48} -78 q^{-49} +15 q^{-50} +59 q^{-51} +25 q^{-52} -6 q^{-53} -10 q^{-54} -8 q^{-55} -5 q^{-56} +9 q^{-57} +2 q^{-58} -4 q^{-59} + q^{-60} </math> |
coloured_jones_6 = <math>q^{84}-4 q^{83}+2 q^{82}+9 q^{81}-5 q^{80}-8 q^{79}-14 q^{78}+14 q^{77}+5 q^{76}+18 q^{75}+64 q^{74}-33 q^{73}-91 q^{72}-142 q^{71}-12 q^{70}+79 q^{69}+240 q^{68}+452 q^{67}+89 q^{66}-372 q^{65}-894 q^{64}-700 q^{63}-286 q^{62}+804 q^{61}+2153 q^{60}+1773 q^{59}+283 q^{58}-2351 q^{57}-3566 q^{56}-3627 q^{55}-523 q^{54}+4727 q^{53}+7138 q^{52}+5812 q^{51}-686 q^{50}-7202 q^{49}-12365 q^{48}-9094 q^{47}+2360 q^{46}+13358 q^{45}+18364 q^{44}+10619 q^{43}-3858 q^{42}-21807 q^{41}-26164 q^{40}-12005 q^{39}+11102 q^{38}+31253 q^{37}+31409 q^{36}+13077 q^{35}-21636 q^{34}-43154 q^{33}-36283 q^{32}-5200 q^{31}+33899 q^{30}+51716 q^{29}+39414 q^{28}-7797 q^{27}-49853 q^{26}-59515 q^{25}-29741 q^{24}+23826 q^{23}+62146 q^{22}+63867 q^{21}+12957 q^{20}-45038 q^{19}-73279 q^{18}-51845 q^{17}+7933 q^{16}+62275 q^{15}+79256 q^{14}+31297 q^{13}-34984 q^{12}-77600 q^{11}-65954 q^{10}-6236 q^9+57322 q^8+86030 q^7+43450 q^6-25252 q^5-76697 q^4-73175 q^3-16550 q^2+51151 q+87709+51151 q^{-1} -16550 q^{-2} -73175 q^{-3} -76697 q^{-4} -25252 q^{-5} +43450 q^{-6} +86030 q^{-7} +57322 q^{-8} -6236 q^{-9} -65954 q^{-10} -77600 q^{-11} -34984 q^{-12} +31297 q^{-13} +79256 q^{-14} +62275 q^{-15} +7933 q^{-16} -51845 q^{-17} -73279 q^{-18} -45038 q^{-19} +12957 q^{-20} +63867 q^{-21} +62146 q^{-22} +23826 q^{-23} -29741 q^{-24} -59515 q^{-25} -49853 q^{-26} -7797 q^{-27} +39414 q^{-28} +51716 q^{-29} +33899 q^{-30} -5200 q^{-31} -36283 q^{-32} -43154 q^{-33} -21636 q^{-34} +13077 q^{-35} +31409 q^{-36} +31253 q^{-37} +11102 q^{-38} -12005 q^{-39} -26164 q^{-40} -21807 q^{-41} -3858 q^{-42} +10619 q^{-43} +18364 q^{-44} +13358 q^{-45} +2360 q^{-46} -9094 q^{-47} -12365 q^{-48} -7202 q^{-49} -686 q^{-50} +5812 q^{-51} +7138 q^{-52} +4727 q^{-53} -523 q^{-54} -3627 q^{-55} -3566 q^{-56} -2351 q^{-57} +283 q^{-58} +1773 q^{-59} +2153 q^{-60} +804 q^{-61} -286 q^{-62} -700 q^{-63} -894 q^{-64} -372 q^{-65} +89 q^{-66} +452 q^{-67} +240 q^{-68} +79 q^{-69} -12 q^{-70} -142 q^{-71} -91 q^{-72} -33 q^{-73} +64 q^{-74} +18 q^{-75} +5 q^{-76} +14 q^{-77} -14 q^{-78} -8 q^{-79} -5 q^{-80} +9 q^{-81} +2 q^{-82} -4 q^{-83} + q^{-84} </math> |
coloured_jones_7 = <math>q^{112}-4 q^{111}+2 q^{110}+9 q^{109}-5 q^{108}-8 q^{107}-14 q^{106}+10 q^{105}+25 q^{104}-2 q^{103}+23 q^{102}+16 q^{101}-46 q^{100}-91 q^{99}-120 q^{98}+q^{97}+194 q^{96}+228 q^{95}+305 q^{94}+159 q^{93}-265 q^{92}-667 q^{91}-1062 q^{90}-701 q^{89}+318 q^{88}+1373 q^{87}+2402 q^{86}+2319 q^{85}+673 q^{84}-1836 q^{83}-4899 q^{82}-5994 q^{81}-3738 q^{80}+996 q^{79}+7628 q^{78}+11884 q^{77}+10820 q^{76}+3971 q^{75}-8456 q^{74}-19772 q^{73}-23149 q^{72}-15565 q^{71}+3896 q^{70}+26043 q^{69}+39541 q^{68}+36591 q^{67}+11339 q^{66}-25804 q^{65}-57204 q^{64}-66358 q^{63}-39973 q^{62}+12511 q^{61}+68336 q^{60}+100926 q^{59}+83792 q^{58}+19179 q^{57}-66151 q^{56}-133172 q^{55}-137679 q^{54}-70621 q^{53}+42889 q^{52}+153359 q^{51}+194934 q^{50}+139172 q^{49}+3442 q^{48}-154136 q^{47}-245138 q^{46}-216584 q^{45}-71245 q^{44}+130992 q^{43}+279711 q^{42}+293462 q^{41}+153405 q^{40}-85147 q^{39}-293239 q^{38}-360206 q^{37}-240305 q^{36}+21900 q^{35}+284890 q^{34}+410240 q^{33}+322851 q^{32}+50497 q^{31}-258503 q^{30}-441071 q^{29}-393503 q^{28}-123370 q^{27}+219717 q^{26}+454109 q^{25}+448852 q^{24}+189820 q^{23}-176053 q^{22}-453071 q^{21}-487746 q^{20}-245868 q^{19}+132559 q^{18}+443069 q^{17}+513256 q^{16}+289741 q^{15}-94142 q^{14}-428270 q^{13}-527350 q^{12}-322834 q^{11}+60878 q^{10}+412390 q^9+535248 q^8+347117 q^7-34348 q^6-396718 q^5-537790 q^4-365850 q^3+10559 q^2+381625 q+539297+381625 q^{-1} +10559 q^{-2} -365850 q^{-3} -537790 q^{-4} -396718 q^{-5} -34348 q^{-6} +347117 q^{-7} +535248 q^{-8} +412390 q^{-9} +60878 q^{-10} -322834 q^{-11} -527350 q^{-12} -428270 q^{-13} -94142 q^{-14} +289741 q^{-15} +513256 q^{-16} +443069 q^{-17} +132559 q^{-18} -245868 q^{-19} -487746 q^{-20} -453071 q^{-21} -176053 q^{-22} +189820 q^{-23} +448852 q^{-24} +454109 q^{-25} +219717 q^{-26} -123370 q^{-27} -393503 q^{-28} -441071 q^{-29} -258503 q^{-30} +50497 q^{-31} +322851 q^{-32} +410240 q^{-33} +284890 q^{-34} +21900 q^{-35} -240305 q^{-36} -360206 q^{-37} -293239 q^{-38} -85147 q^{-39} +153405 q^{-40} +293462 q^{-41} +279711 q^{-42} +130992 q^{-43} -71245 q^{-44} -216584 q^{-45} -245138 q^{-46} -154136 q^{-47} +3442 q^{-48} +139172 q^{-49} +194934 q^{-50} +153359 q^{-51} +42889 q^{-52} -70621 q^{-53} -137679 q^{-54} -133172 q^{-55} -66151 q^{-56} +19179 q^{-57} +83792 q^{-58} +100926 q^{-59} +68336 q^{-60} +12511 q^{-61} -39973 q^{-62} -66358 q^{-63} -57204 q^{-64} -25804 q^{-65} +11339 q^{-66} +36591 q^{-67} +39541 q^{-68} +26043 q^{-69} +3896 q^{-70} -15565 q^{-71} -23149 q^{-72} -19772 q^{-73} -8456 q^{-74} +3971 q^{-75} +10820 q^{-76} +11884 q^{-77} +7628 q^{-78} +996 q^{-79} -3738 q^{-80} -5994 q^{-81} -4899 q^{-82} -1836 q^{-83} +673 q^{-84} +2319 q^{-85} +2402 q^{-86} +1373 q^{-87} +318 q^{-88} -701 q^{-89} -1062 q^{-90} -667 q^{-91} -265 q^{-92} +159 q^{-93} +305 q^{-94} +228 q^{-95} +194 q^{-96} + q^{-97} -120 q^{-98} -91 q^{-99} -46 q^{-100} +16 q^{-101} +23 q^{-102} -2 q^{-103} +25 q^{-104} +10 q^{-105} -14 q^{-106} -8 q^{-107} -5 q^{-108} +9 q^{-109} +2 q^{-110} -4 q^{-111} + q^{-112} </math> |
computer_talk =
<table>
<tr valign=top>
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=    </pre></td>
<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>
</tr>
<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[Knot[8, 18]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td>
<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, 3, 9, 4], X[16, 11, 1, 12], X[2, 14, 3, 13],

X[4, 15, 5, 16], X[10, 6, 11, 5], X[12, 7, 13, 8], X[14, 10, 15, 9]]</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[Knot[8, 18]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[1, -4, 2, -5, 6, -1, 7, -2, 8, -6, 3, -7, 4, -8, 5, -3]</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[Knot[8, 18]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[6, 8, 10, 12, 14, 16, 2, 4]</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>br = BR[Knot[8, 18]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[3, {-1, 2, -1, 2, -1, 2, -1, 2}]</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td>
<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>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{3, 8}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BraidIndex[Knot[8, 18]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>3</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[8, 18]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:8_18_ML.gif]]</td></tr><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> (#[Knot[8, 18]]&) /@ {
SymmetryType, UnknottingNumber, ThreeGenus,
BridgeIndex, SuperBridgeIndex, NakanishiIndex
}</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{FullyAmphicheiral, 2, 3, 3, 4, 2}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -3 5 10 2 3
13 - t + -- - -- - 10 t + 5 t - t
2 t
t</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[8, 18]][z]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4 6
1 + z - z - z</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td>
<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>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[8, 18], Knot[9, 24], Knot[11, NonAlternating, 85],

Knot[11, NonAlternating, 164]}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[8, 18]], KnotSignature[Knot[8, 18]]}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{45, 0}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Jones[Knot[8, 18]][q]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[14]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -4 4 6 7 2 3 4
9 + q - -- + -- - - - 7 q + 6 q - 4 q + q
3 2 q
q q</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td>
<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>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[8, 18]}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[8, 18]][q]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -12 2 -6 -4 4 2 4 6 10 12
1 + q - --- - q - q + -- + 4 q - q - q - 2 q + q
10 2
q q</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[17]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>HOMFLYPT[Knot[8, 18]][a, z]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4
-2 2 2 z 2 2 4 z 2 4 6
3 - a - a - z + -- + a z - 3 z + -- + a z - z
2 2
a a</nowiki></code></td></tr>
</table>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[18]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[8, 18]][a, z]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 3 3
-2 2 z 2 3 z 2 2 4 z 9 z 3
3 + a + a + - + a z + 6 z + ---- + 3 a z - ---- - ---- - 9 a z -
a 2 3 a
a a

4 4 5 5
3 3 4 z 9 z 2 4 4 4 4 z 3 z
4 a z - 20 z + -- - ---- - 9 a z + a z + ---- + ---- +
4 2 3 a
a a a

6 7
5 3 5 6 6 z 2 6 3 z 7
3 a z + 4 a z + 12 z + ---- + 6 a z + ---- + 3 a z
2 a
a</nowiki></code></td></tr>
</table>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[19]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[8, 18]], Vassiliev[3][Knot[8, 18]]}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{1, 0}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[20]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[8, 18]][q, t]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[20]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>5 1 3 1 3 3 4 3
- + 5 q + ----- + ----- + ----- + ----- + ----- + ---- + --- + 3 q t +
q 9 4 7 3 5 3 5 2 3 2 3 q t
q t q t q t q t q t q t

3 3 2 5 2 5 3 7 3 9 4
4 q t + 3 q t + 3 q t + q t + 3 q t + q t</nowiki></code></td></tr>
</table>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[8, 18], 2][q]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -12 4 2 13 21 4 41 38 20 69 43 36
81 + q - --- + --- + -- - -- - -- + -- - -- - -- + -- - -- - -- -
11 10 9 8 7 6 5 4 3 2 q
q q q q q q q q q q

2 3 4 5 6 7 8 9
36 q - 43 q + 69 q - 20 q - 38 q + 41 q - 4 q - 21 q + 13 q +

10 11 12
2 q - 4 q + q</nowiki></code></td></tr>
</table> }}

Knot Atlas - User contributions [en]

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