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{{Rolfsen Knot Page Header|n=10|k=44|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,10,-8,9,-6,3,-4,2,-5,6,-7,8,-9,7,-10,5/goTop.html}}

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{{:{{PAGENAME}} Further Notes and Views}}

{{Knot Presentations}}

<center><table border=1 cellpadding=10><tr align=center valign=top>
<td>
[[Braid Representatives|Minimum Braid Representative]]:
<table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]</td></tr>
</table>

[[Invariants from Braid Theory|Length]] is 10, width is 5.

[[Invariants from Braid Theory|Braid index]] is 5.
</td>
<td>
[[Lightly Documented Features|A Morse Link Presentation]]:

[[Image:{{PAGENAME}}_ML.gif]]
</td>
</tr></table></center>

{{3D Invariants}}
{{4D Invariants}}
{{Polynomial Invariants}}

=== "Similar" Knots (within the Atlas) ===

Same [[The Alexander-Conway Polynomial|Alexander/Conway Polynomial]]:
{[[K11n154]], ...}

Same [[The Jones Polynomial|Jones Polynomial]] (up to mirroring, <math>q\leftrightarrow q^{-1}</math>): 
{...}

{{Vassiliev Invariants}}

{{Khovanov Homology|table=<table border=1>
<tr align=center>
<td width=13.3333%><table cellpadding=0 cellspacing=0>
 <tr><td>\</td><td>&nbsp;</td><td>r</td></tr>
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr>
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr>
</table></td>
 <td width=6.66667%>-6</td  ><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=13.3333%>&chi;</td></tr>
<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>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>1</td></tr>
<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>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>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 bgcolor=yellow>4</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>1</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>5</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>7</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>7</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr>
<tr align=center><td>-5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>-9</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>6</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>
<tr align=center><td>-11</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>&nbsp;</td><td>3</td></tr>
<tr align=center><td>-13</td><td bgcolor=yellow>&nbsp;</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>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>-15</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>
</table>}}

{{Display Coloured Jones|J2=<math>q^{10}-3 q^9+11 q^7-14 q^6-9 q^5+40 q^4-28 q^3-38 q^2+84 q-31-83 q^{-1} +123 q^{-2} -19 q^{-3} -123 q^{-4} +137 q^{-5} +2 q^{-6} -136 q^{-7} +118 q^{-8} +18 q^{-9} -112 q^{-10} +76 q^{-11} +20 q^{-12} -65 q^{-13} +35 q^{-14} +11 q^{-15} -24 q^{-16} +10 q^{-17} +3 q^{-18} -4 q^{-19} + q^{-20} </math>|J3=<math>q^{21}-3 q^{20}+5 q^{18}+6 q^{17}-14 q^{16}-16 q^{15}+23 q^{14}+39 q^{13}-31 q^{12}-76 q^{11}+27 q^{10}+133 q^9-10 q^8-196 q^7-37 q^6+266 q^5+109 q^4-326 q^3-208 q^2+373 q+318-389 q^{-1} -443 q^{-2} +390 q^{-3} +553 q^{-4} -356 q^{-5} -661 q^{-6} +316 q^{-7} +734 q^{-8} -247 q^{-9} -791 q^{-10} +183 q^{-11} +798 q^{-12} -98 q^{-13} -786 q^{-14} +39 q^{-15} +713 q^{-16} +30 q^{-17} -628 q^{-18} -66 q^{-19} +509 q^{-20} +90 q^{-21} -391 q^{-22} -90 q^{-23} +280 q^{-24} +75 q^{-25} -183 q^{-26} -59 q^{-27} +117 q^{-28} +34 q^{-29} -63 q^{-30} -24 q^{-31} +38 q^{-32} +8 q^{-33} -16 q^{-34} -4 q^{-35} +6 q^{-36} +3 q^{-37} -4 q^{-38} + q^{-39} </math>|J4=<math>q^{36}-3 q^{35}+5 q^{33}+6 q^{31}-21 q^{30}-9 q^{29}+23 q^{28}+15 q^{27}+45 q^{26}-76 q^{25}-74 q^{24}+29 q^{23}+66 q^{22}+212 q^{21}-127 q^{20}-251 q^{19}-108 q^{18}+73 q^{17}+621 q^{16}+13 q^{15}-451 q^{14}-534 q^{13}-229 q^{12}+1174 q^{11}+540 q^{10}-343 q^9-1151 q^8-1086 q^7+1499 q^6+1354 q^5+362 q^4-1569 q^3-2386 q^2+1255 q+2061+1595 q^{-1} -1464 q^{-2} -3719 q^{-3} +462 q^{-4} +2343 q^{-5} +2980 q^{-6} -853 q^{-7} -4710 q^{-8} -596 q^{-9} +2170 q^{-10} +4163 q^{-11} +27 q^{-12} -5201 q^{-13} -1633 q^{-14} +1661 q^{-15} +4916 q^{-16} +960 q^{-17} -5115 q^{-18} -2444 q^{-19} +904 q^{-20} +5053 q^{-21} +1765 q^{-22} -4391 q^{-23} -2792 q^{-24} +22 q^{-25} +4428 q^{-26} +2204 q^{-27} -3143 q^{-28} -2508 q^{-29} -699 q^{-30} +3193 q^{-31} +2072 q^{-32} -1802 q^{-33} -1705 q^{-34} -959 q^{-35} +1828 q^{-36} +1469 q^{-37} -821 q^{-38} -826 q^{-39} -772 q^{-40} +825 q^{-41} +778 q^{-42} -328 q^{-43} -253 q^{-44} -425 q^{-45} +304 q^{-46} +308 q^{-47} -137 q^{-48} -31 q^{-49} -166 q^{-50} +100 q^{-51} +91 q^{-52} -59 q^{-53} +10 q^{-54} -46 q^{-55} +28 q^{-56} +21 q^{-57} -19 q^{-58} +4 q^{-59} -8 q^{-60} +6 q^{-61} +3 q^{-62} -4 q^{-63} + q^{-64} </math>|J5=<math>q^{55}-3 q^{54}+5 q^{52}-q^{49}-14 q^{48}-9 q^{47}+23 q^{46}+24 q^{45}+12 q^{44}-9 q^{43}-65 q^{42}-70 q^{41}+22 q^{40}+122 q^{39}+138 q^{38}+43 q^{37}-172 q^{36}-322 q^{35}-176 q^{34}+203 q^{33}+537 q^{32}+479 q^{31}-91 q^{30}-797 q^{29}-973 q^{28}-260 q^{27}+952 q^{26}+1663 q^{25}+964 q^{24}-847 q^{23}-2380 q^{22}-2119 q^{21}+238 q^{20}+3000 q^{19}+3613 q^{18}+990 q^{17}-3126 q^{16}-5280 q^{15}-2988 q^{14}+2585 q^{13}+6814 q^{12}+5533 q^{11}-1080 q^{10}-7839 q^9-8471 q^8-1359 q^7+8064 q^6+11381 q^5+4650 q^4-7300 q^3-13966 q^2-8439 q+5502+15863 q^{-1} +12537 q^{-2} -2878 q^{-3} -17034 q^{-4} -16416 q^{-5} -399 q^{-6} +17299 q^{-7} +20080 q^{-8} +3999 q^{-9} -16985 q^{-10} -23113 q^{-11} -7686 q^{-12} +15981 q^{-13} +25730 q^{-14} +11280 q^{-15} -14703 q^{-16} -27674 q^{-17} -14656 q^{-18} +12992 q^{-19} +29199 q^{-20} +17757 q^{-21} -11142 q^{-22} -29999 q^{-23} -20559 q^{-24} +8861 q^{-25} +30332 q^{-26} +22916 q^{-27} -6433 q^{-28} -29670 q^{-29} -24799 q^{-30} +3546 q^{-31} +28340 q^{-32} +25952 q^{-33} -708 q^{-34} -25834 q^{-35} -26206 q^{-36} -2316 q^{-37} +22673 q^{-38} +25432 q^{-39} +4801 q^{-40} -18696 q^{-41} -23548 q^{-42} -6836 q^{-43} +14531 q^{-44} +20764 q^{-45} +7919 q^{-46} -10396 q^{-47} -17317 q^{-48} -8170 q^{-49} +6797 q^{-50} +13609 q^{-51} +7603 q^{-52} -3928 q^{-53} -10050 q^{-54} -6469 q^{-55} +1893 q^{-56} +6960 q^{-57} +5078 q^{-58} -676 q^{-59} -4489 q^{-60} -3645 q^{-61} -17 q^{-62} +2730 q^{-63} +2471 q^{-64} +189 q^{-65} -1534 q^{-66} -1472 q^{-67} -283 q^{-68} +817 q^{-69} +889 q^{-70} +154 q^{-71} -416 q^{-72} -421 q^{-73} -116 q^{-74} +185 q^{-75} +230 q^{-76} +43 q^{-77} -101 q^{-78} -89 q^{-79} -7 q^{-80} +41 q^{-81} +27 q^{-82} +11 q^{-83} -22 q^{-84} -24 q^{-85} +16 q^{-86} +11 q^{-87} -6 q^{-88} + q^{-89} -8 q^{-91} +6 q^{-92} +3 q^{-93} -4 q^{-94} + q^{-95} </math>|J6=<math>q^{78}-3 q^{77}+5 q^{75}-7 q^{72}+6 q^{71}-14 q^{70}-9 q^{69}+32 q^{68}+15 q^{67}+12 q^{66}-33 q^{65}+2 q^{64}-72 q^{63}-66 q^{62}+91 q^{61}+108 q^{60}+131 q^{59}-33 q^{58}+11 q^{57}-309 q^{56}-380 q^{55}+29 q^{54}+289 q^{53}+607 q^{52}+342 q^{51}+402 q^{50}-695 q^{49}-1367 q^{48}-892 q^{47}-83 q^{46}+1300 q^{45}+1691 q^{44}+2472 q^{43}-26 q^{42}-2600 q^{41}-3618 q^{40}-2988 q^{39}+102 q^{38}+3047 q^{37}+7436 q^{36}+4696 q^{35}-659 q^{34}-6420 q^{33}-9705 q^{32}-7232 q^{31}-713 q^{30}+12265 q^{29}+14728 q^{28}+10054 q^{27}-2164 q^{26}-15416 q^{25}-21664 q^{24}-16449 q^{23}+7434 q^{22}+23201 q^{21}+29811 q^{20}+17128 q^{19}-8188 q^{18}-34063 q^{17}-43344 q^{16}-15944 q^{15}+16075 q^{14}+47133 q^{13}+49424 q^{12}+21236 q^{11}-28709 q^{10}-67765 q^9-54563 q^8-15759 q^7+45187 q^6+79585 q^5+68092 q^4+2930 q^3-72458 q^2-92341 q-66258+16382 q^{-1} +90840 q^{-2} +115705 q^{-3} +53795 q^{-4} -51005 q^{-5} -113407 q^{-6} -118814 q^{-7} -31479 q^{-8} +78152 q^{-9} +149115 q^{-10} +107842 q^{-11} -11482 q^{-12} -113701 q^{-13} -159720 q^{-14} -83318 q^{-15} +49437 q^{-16} +164616 q^{-17} +152757 q^{-18} +32622 q^{-19} -100096 q^{-20} -185587 q^{-21} -128423 q^{-22} +16017 q^{-23} +167286 q^{-24} +185480 q^{-25} +72822 q^{-26} -80895 q^{-27} -199795 q^{-28} -164410 q^{-29} -16471 q^{-30} +161950 q^{-31} +208017 q^{-32} +108189 q^{-33} -58209 q^{-34} -204126 q^{-35} -192503 q^{-36} -49180 q^{-37} +147103 q^{-38} +219668 q^{-39} +139901 q^{-40} -28468 q^{-41} -194144 q^{-42} -210075 q^{-43} -83508 q^{-44} +117205 q^{-45} +213635 q^{-46} +163686 q^{-47} +9697 q^{-48} -163154 q^{-49} -208320 q^{-50} -113417 q^{-51} +71806 q^{-52} +182621 q^{-53} +168745 q^{-54} +47931 q^{-55} -112317 q^{-56} -179615 q^{-57} -126046 q^{-58} +22323 q^{-59} +129644 q^{-60} +147061 q^{-61} +71026 q^{-62} -56021 q^{-63} -128680 q^{-64} -113011 q^{-65} -13560 q^{-66} +71429 q^{-67} +104399 q^{-68} +70000 q^{-69} -13396 q^{-70} -73488 q^{-71} -80596 q^{-72} -26326 q^{-73} +27249 q^{-74} +58558 q^{-75} +50886 q^{-76} +6550 q^{-77} -32092 q^{-78} -45363 q^{-79} -21474 q^{-80} +4673 q^{-81} +25203 q^{-82} +28235 q^{-83} +9299 q^{-84} -10171 q^{-85} -20180 q^{-86} -11394 q^{-87} -1951 q^{-88} +7989 q^{-89} +12213 q^{-90} +5632 q^{-91} -2123 q^{-92} -7224 q^{-93} -4123 q^{-94} -1941 q^{-95} +1675 q^{-96} +4223 q^{-97} +2244 q^{-98} -210 q^{-99} -2181 q^{-100} -904 q^{-101} -850 q^{-102} +104 q^{-103} +1211 q^{-104} +626 q^{-105} +9 q^{-106} -601 q^{-107} -13 q^{-108} -236 q^{-109} -85 q^{-110} +297 q^{-111} +118 q^{-112} -6 q^{-113} -166 q^{-114} +84 q^{-115} -42 q^{-116} -42 q^{-117} +64 q^{-118} +8 q^{-119} -3 q^{-120} -46 q^{-121} +38 q^{-122} - q^{-123} -16 q^{-124} +14 q^{-125} -3 q^{-126} -8 q^{-128} +6 q^{-129} +3 q^{-130} -4 q^{-131} + q^{-132} </math>|J7=<math>q^{105}-3 q^{104}+5 q^{102}-7 q^{99}+6 q^{97}-14 q^{96}+23 q^{94}+15 q^{93}+12 q^{92}-33 q^{91}-33 q^{90}+6 q^{89}-57 q^{88}-8 q^{87}+77 q^{86}+103 q^{85}+139 q^{84}-40 q^{83}-144 q^{82}-117 q^{81}-290 q^{80}-173 q^{79}+116 q^{78}+355 q^{77}+729 q^{76}+415 q^{75}-69 q^{74}-390 q^{73}-1186 q^{72}-1224 q^{71}-660 q^{70}+290 q^{69}+2053 q^{68}+2500 q^{67}+1882 q^{66}+673 q^{65}-2297 q^{64}-4247 q^{63}-4679 q^{62}-3304 q^{61}+1678 q^{60}+5972 q^{59}+8460 q^{58}+8223 q^{57}+1869 q^{56}-5906 q^{55}-12892 q^{54}-16248 q^{53}-9616 q^{52}+2028 q^{51}+15561 q^{50}+26149 q^{49}+22796 q^{48}+8954 q^{47}-12800 q^{46}-35259 q^{45}-40993 q^{44}-29287 q^{43}+52 q^{42}+38471 q^{41}+60676 q^{40}+59020 q^{39}+27160 q^{38}-28566 q^{37}-75247 q^{36}-95423 q^{35}-70757 q^{34}-704 q^{33}+75725 q^{32}+130139 q^{31}+127923 q^{30}+54504 q^{29}-51775 q^{28}-152507 q^{27}-191642 q^{26}-131704 q^{25}-3444 q^{24}+149286 q^{23}+248456 q^{22}+225931 q^{21}+93371 q^{20}-109550 q^{19}-284034 q^{18}-324744 q^{17}-212913 q^{16}+27256 q^{15}+283497 q^{14}+411609 q^{13}+351522 q^{12}+97178 q^{11}-237316 q^{10}-470395 q^9-493271 q^8-255231 q^7+142246 q^6+487946 q^5+620928 q^4+433014 q^3-2703 q^2-457221 q-719351-614408 q^{-1} -170573 q^{-2} +379257 q^{-3} +778790 q^{-4} +782706 q^{-5} +362479 q^{-6} -260086 q^{-7} -795122 q^{-8} -926661 q^{-9} -558534 q^{-10} +112457 q^{-11} +772182 q^{-12} +1038245 q^{-13} +744192 q^{-14} +51137 q^{-15} -716199 q^{-16} -1116948 q^{-17} -911614 q^{-18} -217266 q^{-19} +638985 q^{-20} +1165551 q^{-21} +1054501 q^{-22} +376272 q^{-23} -549427 q^{-24} -1190447 q^{-25} -1174101 q^{-26} -521921 q^{-27} +457764 q^{-28} +1198939 q^{-29} +1271838 q^{-30} +651959 q^{-31} -368307 q^{-32} -1197353 q^{-33} -1353559 q^{-34} -767567 q^{-35} +284212 q^{-36} +1189631 q^{-37} +1422619 q^{-38} +872698 q^{-39} -202848 q^{-40} -1177150 q^{-41} -1483165 q^{-42} -970934 q^{-43} +121095 q^{-44} +1156278 q^{-45} +1534307 q^{-46} +1066833 q^{-47} -32050 q^{-48} -1122699 q^{-49} -1574302 q^{-50} -1159914 q^{-51} -67786 q^{-52} +1067741 q^{-53} +1594747 q^{-54} +1248864 q^{-55} +182852 q^{-56} -985615 q^{-57} -1589043 q^{-58} -1325614 q^{-59} -308921 q^{-60} +870750 q^{-61} +1545461 q^{-62} +1380740 q^{-63} +441973 q^{-64} -724125 q^{-65} -1459885 q^{-66} -1402327 q^{-67} -567724 q^{-68} +551898 q^{-69} +1327561 q^{-70} +1380436 q^{-71} +674572 q^{-72} -366080 q^{-73} -1155586 q^{-74} -1309925 q^{-75} -746710 q^{-76} +183262 q^{-77} +953800 q^{-78} +1191763 q^{-79} +775803 q^{-80} -20303 q^{-81} -740036 q^{-82} -1035078 q^{-83} -757598 q^{-84} -108435 q^{-85} +532499 q^{-86} +854697 q^{-87} +696561 q^{-88} +194535 q^{-89} -348374 q^{-90} -668161 q^{-91} -603277 q^{-92} -237224 q^{-93} +199396 q^{-94} +492786 q^{-95} +492362 q^{-96} +241975 q^{-97} -90679 q^{-98} -341407 q^{-99} -378516 q^{-100} -219195 q^{-101} +20331 q^{-102} +221068 q^{-103} +274214 q^{-104} +181069 q^{-105} +18033 q^{-106} -133320 q^{-107} -187254 q^{-108} -137666 q^{-109} -33225 q^{-110} +73887 q^{-111} +120262 q^{-112} +97677 q^{-113} +34777 q^{-114} -37664 q^{-115} -73292 q^{-116} -64382 q^{-117} -28681 q^{-118} +16976 q^{-119} +41612 q^{-120} +40000 q^{-121} +21478 q^{-122} -6737 q^{-123} -22920 q^{-124} -23237 q^{-125} -13928 q^{-126} +2133 q^{-127} +11462 q^{-128} +12651 q^{-129} +8866 q^{-130} -325 q^{-131} -5799 q^{-132} -6573 q^{-133} -4954 q^{-134} -10 q^{-135} +2611 q^{-136} +3028 q^{-137} +2748 q^{-138} +172 q^{-139} -1152 q^{-140} -1414 q^{-141} -1463 q^{-142} +5 q^{-143} +556 q^{-144} +499 q^{-145} +631 q^{-146} +7 q^{-147} -133 q^{-148} -177 q^{-149} -403 q^{-150} +40 q^{-151} +148 q^{-152} +29 q^{-153} +95 q^{-154} -46 q^{-155} +21 q^{-156} +23 q^{-157} -111 q^{-158} +19 q^{-159} +42 q^{-160} -6 q^{-161} +4 q^{-162} -27 q^{-163} +16 q^{-164} +21 q^{-165} -28 q^{-166} +4 q^{-167} +10 q^{-168} -3 q^{-169} -8 q^{-171} +6 q^{-172} +3 q^{-173} -4 q^{-174} + q^{-175} </math>}}

{{Computer Talk Header}}

<table>
<tr valign=top>
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td>
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
</tr>
<tr valign=top><td colspan=2><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 29, 2005, 15:27:48)...</pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[10, 44]]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[1, 4, 2, 5], X[5, 12, 6, 13], X[3, 11, 4, 10], X[11, 3, 12, 2], 
 
  X[13, 20, 14, 1], X[9, 15, 10, 14], X[15, 18, 16, 19], 
 
  X[7, 16, 8, 17], X[17, 8, 18, 9], X[19, 7, 20, 6]]</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Knot[10, 44]]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[-1, 4, -3, 1, -2, 10, -8, 9, -6, 3, -4, 2, -5, 6, -7, 8, -9, 
 
  7, -10, 5]</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>DTCode[Knot[10, 44]]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>DTCode[4, 10, 12, 16, 14, 2, 20, 18, 8, 6]</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>br = BR[Knot[10, 44]]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[5, {-1, -1, 2, -1, -3, 2, -3, 4, -3, 4}]</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{First[br], Crossings[br]}</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{5, 10}</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>BraidIndex[Knot[10, 44]]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>5</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Knot[10, 44]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_44_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>(#[Knot[10, 44]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, 1, 3, 2, NotAvailable, 1}</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[10, 44]][t]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>       -3   7    19             2    3
-25 + t   - -- + -- + 19 t - 7 t  + t
             2   t
            t</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Knot[10, 44]][z]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>     4    6
1 - z  + z</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[12]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 44], Knot[11, NonAlternating, 154]}</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{KnotDet[Knot[10, 44]], KnotSignature[Knot[10, 44]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{79, -2}</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[14]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Jones[Knot[10, 44]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>      -7   4    7    10   13   13   12            2    3
-9 + q   - -- + -- - -- + -- - -- + -- + 6 q - 3 q  + q
            6    5    4    3    2   q
           q    q    q    q    q</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 44]}</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[16]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Knot[10, 44]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[16]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -22    -20    2     2     2     -12    2     -8   3    2    2
q    - q    - --- + --- - --- + q    + --- - q   + -- - -- + -- - 
               18    16    14           10          6    4    2
              q     q     q            q           q    q    q
 
     2      4    6    10
  2 q  + 2 q  - q  + q</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[17]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>HOMFLYPT[Knot[10, 44]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[17]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                               2
      -2      2    4      2   z       2  2      4  2    6  2      4
-2 + a   + 3 a  - a  - 4 z  + -- + 5 a  z  - 3 a  z  + a  z  - 2 z  + 
                               2
                              a
 
     2  4      4  4    2  6
  3 a  z  - 2 a  z  + a  z</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[18]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[10, 44]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[18]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                                                        2
      -2      2    4   2 z              3        2   3 z        2  2
-2 - a   - 3 a  - a  - --- - 4 a z - 2 a  z + 9 z  + ---- + 13 a  z  + 
                        a                              2
                                                      a
 
                          3
      4  2      6  2   8 z          3       3  3      7  3      4
  10 a  z  + 3 a  z  + ---- + 20 a z  + 15 a  z  - 3 a  z  - 6 z  - 
                        a
 
     4                                              5
  3 z        2  4       4  4      6  4    8  4   9 z          5
  ---- - 12 a  z  - 18 a  z  - 8 a  z  + a  z  - ---- - 26 a z  - 
    2                                             a
   a
 
                                         6
      3  5      5  5      7  5      6   z       2  6      4  6
  27 a  z  - 6 a  z  + 4 a  z  - 4 z  + -- - 7 a  z  + 5 a  z  + 
                                         2
                                        a
 
               7
     6  6   3 z         7       3  7      5  7      8      2  8
  7 a  z  + ---- + 8 a z  + 12 a  z  + 7 a  z  + 3 z  + 7 a  z  + 
             a
 
     4  8      9    3  9
  4 a  z  + a z  + a  z</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[19]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[10, 44]], Vassiliev[3][Knot[10, 44]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[19]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, -1}</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[20]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Knot[10, 44]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[20]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>6    7     1        3        1        4        3       6       4
-- + - + ------ + ------ + ------ + ------ + ----- + ----- + ----- + 
 3   q    15  6    13  5    11  5    11  4    9  4    9  3    7  3
q        q   t    q   t    q   t    q   t    q  t    q  t    q  t
 
    7       6      6      7     4 t                2      3  2
  ----- + ----- + ---- + ---- + --- + 5 q t + 2 q t  + 4 q  t  + 
   7  2    5  2    5      3      q
  q  t    q  t    q  t   q  t
 
   3  3      5  3    7  4
  q  t  + 2 q  t  + q  t</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[21]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>ColouredJones[Knot[10, 44], 2][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[21]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>       -20    4     3    10    24    11    35    65    20    76
-31 + q    - --- + --- + --- - --- + --- + --- - --- + --- + --- - 
              19    18    17    16    15    14    13    12    11
             q     q     q     q     q     q     q     q     q
 
  112   18   118   136   2    137   123   19   123   83
  --- + -- + --- - --- + -- + --- - --- - -- + --- - -- + 84 q - 
   10    9    8     7     6    5     4     3    2    q
  q     q    q     q     q    q     q     q    q
 
      2       3       4      5       6       7      9    10
  38 q  - 28 q  + 40 q  - 9 q  - 14 q  + 11 q  - 3 q  + q</nowiki></pre></td></tr>

</table>

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