6 1

2008-12-16T17:36:19Z

ChiceLtvir: ordommonorr

ricorsitr



{{Rolfsen Knot Page|
n = 6 |
k = 1 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-5,6,-2,3,-4,2,-6,5/goTop.html |
braid_table = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.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:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]</td></tr>
</table> |
braid_crossings = 7 |
braid_width = 4 |
braid_index = 4 |
same_alexander = [[9_46]], [[K11n67]], [[K11n97]], [[K11n139]], |
same_jones = |
khovanov_table = <table border=1>
<tr align=center>
<td width=18.1818%><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=9.09091%>-4</td ><td width=9.09091%>-3</td ><td width=9.09091%>-2</td ><td width=9.09091%>-1</td ><td width=9.09091%>0</td ><td width=9.09091%>1</td ><td width=9.09091%>2</td ><td width=18.1818%>χ</td></tr>
<tr align=center><td>5</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>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td>0</td></tr>
<tr align=center><td>1</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow>1</td><td> </td><td>1</td></tr>
<tr align=center><td>-1</td><td> </td><td> </td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>1</td><td> </td><td> </td><td>0</td></tr>
<tr align=center><td>-3</td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow>1</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>1</td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
<tr align=center><td>-7</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</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>1</td></tr>
</table> |
coloured_jones_2 = <math>q^6-q^5+2 q^3-3 q^2+4-4 q^{-1} +4 q^{-3} -3 q^{-4} +3 q^{-6} -2 q^{-7} - q^{-8} +2 q^{-9} - q^{-10} - q^{-11} + q^{-12} </math> |
coloured_jones_3 = <math>q^{12}-q^{11}+q^8-2 q^7+2 q^5+q^4-4 q^3+4 q+2-5 q^{-1} - q^{-2} +5 q^{-3} + q^{-4} -4 q^{-5} -2 q^{-6} +4 q^{-7} + q^{-8} -3 q^{-9} -2 q^{-10} +3 q^{-11} +2 q^{-12} -2 q^{-13} -2 q^{-14} + q^{-15} +3 q^{-16} - q^{-17} -2 q^{-18} +2 q^{-20} - q^{-22} - q^{-23} + q^{-24} </math> |
coloured_jones_4 = <math>q^{20}-q^{19}-q^{16}+2 q^{15}-2 q^{14}+q^{13}+q^{12}-2 q^{11}+2 q^{10}-4 q^9+3 q^8+4 q^7-3 q^6+q^5-7 q^4+4 q^3+6 q^2-3 q+2-10 q^{-1} +4 q^{-2} +7 q^{-3} -3 q^{-4} +2 q^{-5} -10 q^{-6} +4 q^{-7} +6 q^{-8} -3 q^{-9} +3 q^{-10} -8 q^{-11} +3 q^{-12} +5 q^{-13} -2 q^{-14} +3 q^{-15} -7 q^{-16} + q^{-17} +3 q^{-18} - q^{-19} +4 q^{-20} -6 q^{-21} + q^{-23} +5 q^{-25} -4 q^{-26} - q^{-27} - q^{-28} +5 q^{-30} -2 q^{-31} - q^{-32} - q^{-33} - q^{-34} +3 q^{-35} - q^{-38} - q^{-39} + q^{-40} </math> |
coloured_jones_5 = <math>q^{30}-q^{29}-q^{26}+2 q^{24}-q^{23}+q^{21}-2 q^{20}-q^{19}+2 q^{18}+2 q^{16}+2 q^{15}-3 q^{14}-4 q^{13}-q^{12}+2 q^{11}+5 q^{10}+5 q^9-4 q^8-7 q^7-4 q^6+q^5+8 q^4+7 q^3-3 q^2-8 q-5+8 q^{-2} +8 q^{-3} - q^{-4} -8 q^{-5} -7 q^{-6} + q^{-7} +8 q^{-8} +6 q^{-9} -8 q^{-11} -6 q^{-12} +2 q^{-13} +7 q^{-14} +4 q^{-15} -7 q^{-17} -5 q^{-18} + q^{-19} +5 q^{-20} +3 q^{-21} + q^{-22} -4 q^{-23} -4 q^{-24} +3 q^{-26} +3 q^{-27} + q^{-28} - q^{-29} -2 q^{-30} -2 q^{-31} +2 q^{-33} + q^{-34} + q^{-35} -2 q^{-37} -2 q^{-38} +3 q^{-41} +2 q^{-42} - q^{-43} -2 q^{-44} -2 q^{-45} - q^{-46} +2 q^{-47} +3 q^{-48} - q^{-50} - q^{-51} -2 q^{-52} +2 q^{-54} + q^{-55} - q^{-58} - q^{-59} + q^{-60} </math> |
coloured_jones_6 = <math>q^{42}-q^{41}-q^{38}+3 q^{35}-2 q^{34}+q^{32}-2 q^{31}-q^{30}+5 q^{28}-2 q^{27}+q^{26}+2 q^{25}-5 q^{24}-4 q^{23}-q^{22}+8 q^{21}+4 q^{19}+4 q^{18}-10 q^{17}-9 q^{16}-5 q^{15}+11 q^{14}+4 q^{13}+9 q^{12}+8 q^{11}-14 q^{10}-14 q^9-9 q^8+12 q^7+5 q^6+13 q^5+12 q^4-15 q^3-16 q^2-12 q+13+3 q^{-1} +14 q^{-2} +15 q^{-3} -15 q^{-4} -16 q^{-5} -13 q^{-6} +12 q^{-7} +2 q^{-8} +14 q^{-9} +15 q^{-10} -15 q^{-11} -16 q^{-12} -12 q^{-13} +13 q^{-14} +2 q^{-15} +13 q^{-16} +13 q^{-17} -14 q^{-18} -15 q^{-19} -11 q^{-20} +13 q^{-21} +2 q^{-22} +11 q^{-23} +11 q^{-24} -11 q^{-25} -12 q^{-26} -10 q^{-27} +11 q^{-28} +9 q^{-30} +10 q^{-31} -8 q^{-32} -9 q^{-33} -9 q^{-34} +8 q^{-35} -3 q^{-36} +7 q^{-37} +9 q^{-38} -4 q^{-39} -6 q^{-40} -7 q^{-41} +6 q^{-42} -6 q^{-43} +5 q^{-44} +7 q^{-45} - q^{-46} -2 q^{-47} -4 q^{-48} +5 q^{-49} -8 q^{-50} +2 q^{-51} +4 q^{-52} - q^{-55} +6 q^{-56} -7 q^{-57} - q^{-58} + q^{-62} +7 q^{-63} -4 q^{-64} - q^{-65} -2 q^{-66} - q^{-67} - q^{-68} +6 q^{-70} - q^{-71} - q^{-73} - q^{-74} -2 q^{-75} - q^{-76} +3 q^{-77} + q^{-79} - q^{-82} - q^{-83} + q^{-84} </math> |
coloured_jones_7 = <math>q^{56}-q^{55}-q^{52}+q^{49}+2 q^{48}-2 q^{47}+q^{45}-2 q^{44}-q^{42}+2 q^{41}+4 q^{40}-3 q^{39}+q^{37}-4 q^{36}-q^{35}-2 q^{34}+4 q^{33}+7 q^{32}-q^{31}-2 q^{29}-9 q^{28}-3 q^{27}-3 q^{26}+6 q^{25}+15 q^{24}+4 q^{23}+3 q^{22}-7 q^{21}-17 q^{20}-9 q^{19}-7 q^{18}+10 q^{17}+23 q^{16}+11 q^{15}+8 q^{14}-8 q^{13}-25 q^{12}-16 q^{11}-11 q^{10}+10 q^9+28 q^8+14 q^7+14 q^6-7 q^5-28 q^4-19 q^3-15 q^2+8 q+30+15 q^{-1} +16 q^{-2} -5 q^{-3} -28 q^{-4} -18 q^{-5} -17 q^{-6} +6 q^{-7} +29 q^{-8} +16 q^{-9} +17 q^{-10} -6 q^{-11} -28 q^{-12} -16 q^{-13} -16 q^{-14} +5 q^{-15} +29 q^{-16} +17 q^{-17} +15 q^{-18} -7 q^{-19} -28 q^{-20} -14 q^{-21} -15 q^{-22} +5 q^{-23} +28 q^{-24} +16 q^{-25} +13 q^{-26} -7 q^{-27} -26 q^{-28} -12 q^{-29} -14 q^{-30} +4 q^{-31} +24 q^{-32} +14 q^{-33} +12 q^{-34} -5 q^{-35} -22 q^{-36} -10 q^{-37} -12 q^{-38} + q^{-39} +19 q^{-40} +11 q^{-41} +13 q^{-42} - q^{-43} -17 q^{-44} -8 q^{-45} -12 q^{-46} -2 q^{-47} +14 q^{-48} +7 q^{-49} +12 q^{-50} +4 q^{-51} -11 q^{-52} -6 q^{-53} -11 q^{-54} -5 q^{-55} +9 q^{-56} +2 q^{-57} +10 q^{-58} +7 q^{-59} -6 q^{-60} -2 q^{-61} -8 q^{-62} -6 q^{-63} +4 q^{-64} -2 q^{-65} +6 q^{-66} +7 q^{-67} -3 q^{-68} +2 q^{-69} -3 q^{-70} -4 q^{-71} +2 q^{-72} -5 q^{-73} +2 q^{-74} +4 q^{-75} -3 q^{-76} +3 q^{-77} + q^{-78} +3 q^{-80} -5 q^{-81} - q^{-82} + q^{-83} -5 q^{-84} +2 q^{-85} + q^{-86} +2 q^{-87} +5 q^{-88} -2 q^{-89} - q^{-90} -4 q^{-92} - q^{-93} - q^{-94} + q^{-95} +5 q^{-96} + q^{-99} -2 q^{-100} - q^{-101} -2 q^{-102} - q^{-103} +2 q^{-104} + q^{-105} + q^{-107} - q^{-110} - 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[6, 1]]</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[1, 4, 2, 5], X[7, 10, 8, 11], X[3, 9, 4, 8], X[9, 3, 10, 2],

X[5, 12, 6, 1], X[11, 6, 12, 7]]</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[6, 1]]</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, -3, 1, -5, 6, -2, 3, -4, 2, -6, 5]</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[6, 1]]</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[4, 8, 12, 10, 2, 6]</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[6, 1]]</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[4, {-1, -1, -2, 1, 3, -2, 3}]</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>{4, 7}</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[6, 1]]</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>4</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[6, 1]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:6_1_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[6, 1]]&) /@ {
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>{Reversible, 1, 1, 2, {3, 4}, 1}</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[6, 1]][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> 2
5 - - - 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[6, 1]][z]</nowiki></code></td></tr>
<tr align=left>
<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
1 - 2 z</nowiki></code></td></tr>
</table>
<table><tr align=left>
<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>
<tr align=left>
<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[6, 1], Knot[9, 46], Knot[11, NonAlternating, 67],

Knot[11, NonAlternating, 97], Knot[11, NonAlternating, 139]}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<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[6, 1]], KnotSignature[Knot[6, 1]]}</nowiki></code></td></tr>
<tr align=left>
<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>{9, 0}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<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[6, 1]][q]</nowiki></code></td></tr>
<tr align=left>
<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 -3 -2 2 2
2 + q - q + q - - - q + q
q</nowiki></code></td></tr>
</table>
<table><tr align=left>
<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>
<tr align=left>
<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[6, 1]}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<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[6, 1]][q]</nowiki></code></td></tr>
<tr align=left>
<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> -14 -12 -6 -4 2 6 8
q + q - q - q + q + q + q</nowiki></code></td></tr>
</table>
<table><tr align=left>
<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[6, 1]][a, z]</nowiki></code></td></tr>
<tr align=left>
<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 2 4 2 2 2
a - a + a - z - a z</nowiki></code></td></tr>
</table>
<table><tr align=left>
<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[6, 1]][a, z]</nowiki></code></td></tr>
<tr align=left>
<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
-2 2 4 3 z 2 2 4 2 z
-a + a + a + 2 a z + 2 a z + -- - 4 a z - 3 a z + -- -
2 a
a

3 3 3 4 2 4 4 4 5 3 5
2 a z - 3 a z + z + 2 a z + a z + a z + a z</nowiki></code></td></tr>
</table>
<table><tr align=left>
<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[6, 1]], Vassiliev[3][Knot[6, 1]]}</nowiki></code></td></tr>
<tr align=left>
<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>{-2, 1}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<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[6, 1]][q, t]</nowiki></code></td></tr>
<tr align=left>
<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>1 1 1 1 1 1 5 2
- + 2 q + ----- + ----- + ----- + ---- + --- + q t + q t
q 9 4 5 3 5 2 3 q t
q t q t q t q t</nowiki></code></td></tr>
</table>
<table><tr align=left>
<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[6, 1], 2][q]</nowiki></code></td></tr>
<tr align=left>
<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 -11 -10 2 -8 2 3 3 4 4 2
4 + q - q - q + -- - q - -- + -- - -- + -- - - - 3 q +
9 7 6 4 3 q
q q q q q

3 5 6
2 q - q + q</nowiki></code></td></tr>
</table> }}

Knot Atlas - User contributions [en]

6 1