K11n66: Difference between revisions

From Knot Atlas
Jump to navigationJump to search
No edit summary
 
No edit summary
Line 1: Line 1:
<!-- WARNING! WARNING! WARNING!
<!-- This page was generated from the splice template "Hoste-Thistlethwaite_Splice_Template". Please do not edit! -->
<!-- This page was generated from the splice base [[Hoste-Thistlethwaite_Splice_Base]]. Please do not edit!
<!-- --> <!--
<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)
-->
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Hoste-Thistlethwaite_Splice_Base]]. -->
<!-- -->
<!-- -->
<!-- WARNING! WARNING! WARNING!
<!-- This page was generated from the splice template [[Hoste-Thistlethwaite Splice Template]]. Please do not edit!
<!-- Almost certainly, you want to edit [[Template:Hoste-Thistlethwaite Knot Page]], which actually produces this page.
<!-- The text below simply calls [[Template:Hoste-Thistlethwaite Knot Page]] setting the values of all the parameters appropriately.
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Hoste-Thistlethwaite Splice Template]]. -->
<!-- -->
{{Hoste-Thistlethwaite Knot Page|
{{Hoste-Thistlethwaite Knot Page|
n = 11 |
n = 11 |
t = n |
t = <nowiki>n</nowiki> |
k = 66 |
k = 66 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,2,-1,3,-8,4,-2,-5,9,-6,-11,7,-3,8,6,-9,5,10,-7,11,-10/goTop.html |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,2,-1,3,-8,4,-2,-5,9,-6,-11,7,-3,8,6,-9,5,10,-7,11,-10/goTop.html |
Line 41: Line 50:
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
</tr>
</tr>
<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</td></tr>
<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr>
</table>
<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>Crossings[Knot[11, NonAlternating, 66]]</nowiki></pre></td></tr>
<table><tr align=left>
<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>11</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>PD[Knot[11, NonAlternating, 66]]</nowiki></pre></td></tr>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td>
<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>PD[X[4, 2, 5, 1], X[8, 4, 9, 3], X[14, 5, 15, 6], X[2, 8, 3, 7],
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Crossings[Knot[11, NonAlternating, 66]]</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>11</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>PD[Knot[11, NonAlternating, 66]]</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>PD[X[4, 2, 5, 1], X[8, 4, 9, 3], X[14, 5, 15, 6], X[2, 8, 3, 7],
X[9, 19, 10, 18], X[11, 17, 12, 16], X[20, 14, 21, 13],
X[9, 19, 10, 18], X[11, 17, 12, 16], X[20, 14, 21, 13],
Line 51: Line 70:
X[6, 15, 7, 16], X[17, 11, 18, 10], X[22, 19, 1, 20],
X[6, 15, 7, 16], X[17, 11, 18, 10], X[22, 19, 1, 20],
X[12, 22, 13, 21]]</nowiki></pre></td></tr>
X[12, 22, 13, 21]]</nowiki></code></td></tr>
</table>
<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>GaussCode[Knot[11, NonAlternating, 66]]</nowiki></pre></td></tr>
<table><tr align=left>
<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>GaussCode[1, -4, 2, -1, 3, -8, 4, -2, -5, 9, -6, -11, 7, -3, 8, 6, -9,
<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>GaussCode[Knot[11, NonAlternating, 66]]</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>GaussCode[1, -4, 2, -1, 3, -8, 4, -2, -5, 9, -6, -11, 7, -3, 8, 6, -9,
5, 10, -7, 11, -10]</nowiki></pre></td></tr>
5, 10, -7, 11, -10]</nowiki></code></td></tr>
</table>
<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[Knot[11, NonAlternating, 66]]</nowiki></pre></td></tr>
<table><tr align=left>
<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[Knot[11, NonAlternating, 66]]</nowiki></pre></td></tr>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td>
<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>Show[DrawMorseLink[Knot[11, NonAlternating, 66]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:K11n66_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[6]=</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[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[11, NonAlternating, 66]][t]</nowiki></pre></td></tr>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[Knot[11, NonAlternating, 66]]</nowiki></code></td></tr>
<tr align=left>
<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> -3 7 18 2 3
<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[Knot[11, NonAlternating, 66]]</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>Show[DrawMorseLink[Knot[11, NonAlternating, 66]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:K11n66_ML.gif]]</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>-Graphics-</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>alex = Alexander[Knot[11, NonAlternating, 66]][t]</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 7 18 2 3
-23 + t - -- + -- + 18 t - 7 t + t
-23 + t - -- + -- + 18 t - 7 t + t
2 t
2 t
t</nowiki></pre></td></tr>
t</nowiki></code></td></tr>
</table>
<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>Conway[Knot[11, NonAlternating, 66]][z]</nowiki></pre></td></tr>
<table><tr align=left>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td>
1 - z - z + z</nowiki></pre></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>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[11, NonAlternating, 66]][z]</nowiki></code></td></tr>
<tr align=left>
<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>{Knot[9, 40], Knot[10, 59], Knot[11, NonAlternating, 66]}</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>{KnotDet[Knot[11, NonAlternating, 66]], KnotSignature[Knot[11, NonAlternating, 66]]}</nowiki></pre></td></tr>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td>
<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>{75, 2}</nowiki></pre></td></tr>
<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>
<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>J=Jones[Knot[11, NonAlternating, 66]][q]</nowiki></pre></td></tr>
</table>
<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> -2 4 2 3 4 5 6 7
<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>Select[AllKnots[], (alex === Alexander[#][t])&]</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>{Knot[9, 40], Knot[10, 59], Knot[11, NonAlternating, 66]}</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>{KnotDet[Knot[11, NonAlternating, 66]], KnotSignature[Knot[11, NonAlternating, 66]]}</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>{75, 2}</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>J=Jones[Knot[11, NonAlternating, 66]][q]</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 4 2 3 4 5 6 7
-7 - q + - + 11 q - 12 q + 13 q - 12 q + 8 q - 5 q + 2 q
-7 - q + - + 11 q - 12 q + 13 q - 12 q + 8 q - 5 q + 2 q
q</nowiki></pre></td></tr>
q</nowiki></code></td></tr>
</table>
<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[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr>
<table><tr align=left>
<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[11, NonAlternating, 66], Knot[11, NonAlternating, 150]}</nowiki></pre></td></tr>
<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[], (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[12]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[11, NonAlternating, 66], Knot[11, NonAlternating, 150]}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<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>A2Invariant[Knot[11, NonAlternating, 66]][q]</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> -6 2 -2 2 4 6 8 10 12 14 16
<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>A2Invariant[Knot[11, NonAlternating, 66]][q]</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> -6 2 -2 2 4 6 8 10 12 14 16
-q + -- - q + 4 q - q + 4 q - q - q - q - 4 q + 2 q -
-q + -- - q + 4 q - q + 4 q - q - q - q - 4 q + 2 q -
4
4
Line 85: Line 155:
18 22
18 22
q + 2 q</nowiki></pre></td></tr>
q + 2 q</nowiki></code></td></tr>
</table>
<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>Kauffman[Knot[11, NonAlternating, 66]][a, z]</nowiki></pre></td></tr>
<table><tr align=left>
<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> 2 2 2 2
<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>Kauffman[Knot[11, NonAlternating, 66]][a, z]</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> 2 2 2 2
-2 5 4 3 z 4 z z 2 4 z z 14 z 12 z
-2 5 4 3 z 4 z z 2 4 z z 14 z 12 z
-- - -- - -- + --- + --- - - + 3 z - ---- + -- + ----- + ----- -
-- - -- - -- + --- + --- - - + 3 z - ---- + -- + ----- + ----- -
Line 109: Line 184:
---- + ---- + ---- + ---- + -- + --
---- + ---- + ---- + ---- + -- + --
a 6 4 2 5 3
a 6 4 2 5 3
a a a a a</nowiki></pre></td></tr>
a a a a a</nowiki></code></td></tr>
</table>
<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>{Vassiliev[2][Knot[11, NonAlternating, 66]], Vassiliev[3][Knot[11, NonAlternating, 66]]}</nowiki></pre></td></tr>
<table><tr align=left>
<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>{-1, -3}</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>Kh[Knot[11, NonAlternating, 66]][q, t]</nowiki></pre></td></tr>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td>
<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> 3 1 3 1 4 3 q 3 5
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[11, NonAlternating, 66]], Vassiliev[3][Knot[11, NonAlternating, 66]]}</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>{-1, -3}</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>Kh[Knot[11, NonAlternating, 66]][q, t]</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> 3 1 3 1 4 3 q 3 5
7 q + 5 q + ----- + ----- + ---- + --- + --- + 6 q t + 6 q t +
7 q + 5 q + ----- + ----- + ---- + --- + --- + 6 q t + 6 q t +
5 3 3 2 2 q t t
5 3 3 2 2 q t t
Line 122: Line 207:
11 5 13 5 15 6
11 5 13 5 15 6
2 q t + 3 q t + 2 q t</nowiki></pre></td></tr>
2 q t + 3 q t + 2 q t</nowiki></code></td></tr>
</table> }}
</table> }}

Revision as of 16:12, 1 September 2005

K11n65.gif

K11n65

K11n67.gif

K11n67

K11n66.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n66 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X8493 X14,5,15,6 X2837 X9,19,10,18 X11,17,12,16 X20,14,21,13 X6,15,7,16 X17,11,18,10 X22,19,1,20 X12,22,13,21
Gauss code 1, -4, 2, -1, 3, -8, 4, -2, -5, 9, -6, -11, 7, -3, 8, 6, -9, 5, 10, -7, 11, -10
Dowker-Thistlethwaite code 4 8 14 2 -18 -16 20 6 -10 22 12
A Braid Representative {{{braid_table}}}
A Morse Link Presentation K11n66 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11n66/ThurstonBennequinNumber
Hyperbolic Volume 14.4341
A-Polynomial See Data:K11n66/A-polynomial

[edit Notes for K11n66's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant -2

[edit Notes for K11n66's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 75, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n66/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n66/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {9_40, 10_59,}

Same Jones Polynomial (up to mirroring, ): {K11n150,}

Vassiliev invariants

V2 and V3: (-1, -3)
V2,1 through V6,9:
V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9

V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.

Khovanov Homology

The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where 2 is the signature of K11n66. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-3-2-10123456χ
15         22
13        3 -3
11       52 3
9      73  -4
7     65   1
5    67    1
3   56     -1
1  37      4
-1 14       -3
-3 3        3
-51         -1
Integral Khovanov Homology

(db, data source)

  

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.

Modifying This Page

Read me first: Modifying Knot Pages.

See/edit the Hoste-Thistlethwaite Knot Page master template (intermediate).

See/edit the Hoste-Thistlethwaite_Splice_Base (expert).

Back to the top.

K11n65.gif

K11n65

K11n67.gif

K11n67