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Knot Atlas - User contributions [en]
2026-04-07T21:46:49Z
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https://katlas.org/index.php?title=L9n28&diff=1693828
L9n28
2009-05-27T08:59:25Z
<p>BascoBocno: </p>
<hr />
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<!-- WARNING! WARNING! WARNING!<br />
<!-- This page was generated from the splice template [[Link_Splice_Base]]. Please do not edit!<br />
<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)<br />
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Link_Splice_Base]]. --><br />
<!-- <math>\text{Null}</math> --><br />
<!-- <math>\text{Null}</math> --><br />
<!-- WARNING! WARNING! WARNING!<br />
<!-- This page was generated from the splice template [[Link Splice Template]]. Please do not edit!<br />
<!-- Almost certainly, you want to edit [[Template:Link Page]], which actually produces this page.<br />
<!-- The text below simply calls [[Template:Link Page]] setting the values of all the parameters appropriately.<br />
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Link Splice Template]]. --><br />
<!-- <math>\text{Null}</math> --><br />
{{Link Page|<br />
n = 9 |<br />
t = n |<br />
k = 28 |<br />
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,5,-3:8,6,-7,-4:-6,-1,2,-5,4,-8,9,-2,3,7/goTop.html |<br />
braid_table = <table cellspacing=0 cellpadding=0 border=0 style="white-space: pre"><br />
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]]</td></tr><br />
</table> |<br />
khovanov_table = <table border=1><br />
<tr align=center><br />
<td width=16.6667%><table cellpadding=0 cellspacing=0><br />
<tr><td>\</td><td>&nbsp;</td><td>r</td></tr><br />
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr><br />
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr><br />
</table></td><br />
<td width=8.33333%>-3</td ><td width=8.33333%>-2</td ><td width=8.33333%>-1</td ><td width=8.33333%>0</td ><td width=8.33333%>1</td ><td width=8.33333%>2</td ><td width=8.33333%>3</td ><td width=8.33333%>4</td ><td width=16.6667%>&chi;</td></tr><br />
<tr align=center><td>11</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td>3</td></tr><br />
<tr align=center><td>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>2</td><td>-1</td></tr><br />
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>-1</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
<tr align=center><td>-3</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>-5</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>-1</td></tr><br />
</table> |<br />
computer_talk =<br />
<table><br />
<tr valign=top><br />
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td><br />
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td><br />
</tr><br />
<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 3, 2005, 2:11:43)...</td></tr><br />
<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[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>9</nowiki></pre></td></tr><br />
<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>Length[Skeleton[Link[9, NonAlternating, 28]]]</nowiki></pre></td></tr><br />
<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>3</nowiki></pre></td></tr><br />
<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>PD[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>PD[X[6, 1, 7, 2], X[12, 7, 13, 8], X[4, 13, 1, 14], X[18, 10, 15, 9], <br />
<br />
X[8, 4, 9, 3], X[5, 17, 6, 16], X[17, 5, 18, 14], X[10, 16, 11, 15], <br />
<br />
X[2, 12, 3, 11]]</nowiki></pre></td></tr><br />
<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>GaussCode[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>GaussCode[{1, -9, 5, -3}, {8, 6, -7, -4}, <br />
<br />
{-6, -1, 2, -5, 4, -8, 9, -2, 3, 7}]</nowiki></pre></td></tr><br />
<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>BR[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>BR[4, {1, 2, 3, 3, 2, -1, -2, 3, -2, 3, -2}]</nowiki></pre></td></tr><br />
<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>Show[DrawMorseLink[Link[9, NonAlternating, 28]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L9n28_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[7]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr><br />
<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>KnotSignature[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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</nowiki></pre></td></tr><br />
<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>J=Jones[Link[9, NonAlternating, 28]][q]</nowiki></pre></td></tr><br />
<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> -2 3 2 3 4 5<br />
-4 - q + - + 6 q - 5 q + 6 q - 4 q + 3 q<br />
q</nowiki></pre></td></tr><br />
<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>A2Invariant[Link[9, NonAlternating, 28]][q]</nowiki></pre></td></tr><br />
<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> -6 -4 2 6 8 10 12 14 16<br />
1 - q + q + 2 q + 4 q + 2 q + 5 q + 4 q + 3 q + 4 q + <br />
<br />
18 20<br />
q + q</nowiki></pre></td></tr><br />
<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>HOMFLYPT[Link[9, NonAlternating, 28]][a, z]</nowiki></pre></td></tr><br />
<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 2 4<br />
-6 4 3 1 2 1 2 3 z 5 z 4 z<br />
a - -- + -- + ----- - ----- + ----- - 2 z - ---- + ---- - z - -- + <br />
4 2 6 2 4 2 2 2 4 2 4<br />
a a a z a z a z a a a<br />
<br />
4 6<br />
4 z z<br />
---- + --<br />
2 2<br />
a a</nowiki></pre></td></tr><br />
<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>Kauffman[Link[9, NonAlternating, 28]][a, z]</nowiki></pre></td></tr><br />
<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> 5 10 7 1 2 1 2 2 5 z 7 z<br />
-1 - -- - -- - -- + ----- + ----- + ----- - ---- - ---- + --- + --- + <br />
6 4 2 6 2 4 2 2 2 5 3 5 3<br />
a a a a z a z a z a z a z a a<br />
<br />
2 2 2 3 3 3<br />
3 z 2 6 z 18 z 17 z 3 z 8 z 7 z<br />
--- + a z + 5 z + ---- + ----- + ----- - ---- - ---- - ---- - <br />
a 6 4 2 5 3 a<br />
a a a a a<br />
<br />
4 4 5 5 5 6<br />
3 4 13 z 21 z 3 z z z 5 6 5 z<br />
2 a z - 8 z - ----- - ----- + ---- + -- - -- + a z + 3 z + ---- + <br />
4 2 5 3 a 4<br />
a a a a a<br />
<br />
6 7 7<br />
8 z 2 z 2 z<br />
---- + ---- + ----<br />
2 3 a<br />
a a</nowiki></pre></td></tr><br />
<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>Kh[Link[9, NonAlternating, 28]][q, t]</nowiki></pre></td></tr><br />
<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> 3 1 2 1 2 2 q 3 5<br />
4 q + 4 q + ----- + ----- + ---- + --- + --- + 3 q t + 2 q t + <br />
5 3 3 2 2 q t t<br />
q t q t q t<br />
<br />
5 2 7 2 7 3 9 3 9 4 11 4<br />
3 q t + 3 q t + q t + 3 q t + 2 q t + 3 q t</nowiki></pre></td></tr><br />
</table> }}</div>
BascoBocno
https://katlas.org/index.php?title=L9n28&diff=1693796
L9n28
2009-05-26T12:09:38Z
<p>BascoBocno: </p>
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http://www.textdompasrold.com <br />
<!-- WARNING! WARNING! WARNING!<br />
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<!-- <math>\text{Null}</math> --><br />
{{Link Page|<br />
n = 9 |<br />
t = n |<br />
k = 28 |<br />
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,5,-3:8,6,-7,-4:-6,-1,2,-5,4,-8,9,-2,3,7/goTop.html |<br />
braid_table = <table cellspacing=0 cellpadding=0 border=0 style="white-space: pre"><br />
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]]</td></tr><br />
</table> |<br />
khovanov_table = <table border=1><br />
<tr align=center><br />
<td width=16.6667%><table cellpadding=0 cellspacing=0><br />
<tr><td>\</td><td>&nbsp;</td><td>r</td></tr><br />
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr><br />
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr><br />
</table></td><br />
<td width=8.33333%>-3</td ><td width=8.33333%>-2</td ><td width=8.33333%>-1</td ><td width=8.33333%>0</td ><td width=8.33333%>1</td ><td width=8.33333%>2</td ><td width=8.33333%>3</td ><td width=8.33333%>4</td ><td width=16.6667%>&chi;</td></tr><br />
<tr align=center><td>11</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td>3</td></tr><br />
<tr align=center><td>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>2</td><td>-1</td></tr><br />
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>-1</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
<tr align=center><td>-3</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>-5</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>-1</td></tr><br />
</table> |<br />
computer_talk =<br />
<table><br />
<tr valign=top><br />
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td><br />
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td><br />
</tr><br />
<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 3, 2005, 2:11:43)...</td></tr><br />
<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[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>9</nowiki></pre></td></tr><br />
<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>Length[Skeleton[Link[9, NonAlternating, 28]]]</nowiki></pre></td></tr><br />
<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>3</nowiki></pre></td></tr><br />
<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>PD[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>PD[X[6, 1, 7, 2], X[12, 7, 13, 8], X[4, 13, 1, 14], X[18, 10, 15, 9], <br />
<br />
X[8, 4, 9, 3], X[5, 17, 6, 16], X[17, 5, 18, 14], X[10, 16, 11, 15], <br />
<br />
X[2, 12, 3, 11]]</nowiki></pre></td></tr><br />
<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>GaussCode[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>GaussCode[{1, -9, 5, -3}, {8, 6, -7, -4}, <br />
<br />
{-6, -1, 2, -5, 4, -8, 9, -2, 3, 7}]</nowiki></pre></td></tr><br />
<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>BR[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>BR[4, {1, 2, 3, 3, 2, -1, -2, 3, -2, 3, -2}]</nowiki></pre></td></tr><br />
<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>Show[DrawMorseLink[Link[9, NonAlternating, 28]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L9n28_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[7]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr><br />
<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>KnotSignature[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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</nowiki></pre></td></tr><br />
<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>J=Jones[Link[9, NonAlternating, 28]][q]</nowiki></pre></td></tr><br />
<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> -2 3 2 3 4 5<br />
-4 - q + - + 6 q - 5 q + 6 q - 4 q + 3 q<br />
q</nowiki></pre></td></tr><br />
<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>A2Invariant[Link[9, NonAlternating, 28]][q]</nowiki></pre></td></tr><br />
<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> -6 -4 2 6 8 10 12 14 16<br />
1 - q + q + 2 q + 4 q + 2 q + 5 q + 4 q + 3 q + 4 q + <br />
<br />
18 20<br />
q + q</nowiki></pre></td></tr><br />
<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>HOMFLYPT[Link[9, NonAlternating, 28]][a, z]</nowiki></pre></td></tr><br />
<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 2 4<br />
-6 4 3 1 2 1 2 3 z 5 z 4 z<br />
a - -- + -- + ----- - ----- + ----- - 2 z - ---- + ---- - z - -- + <br />
4 2 6 2 4 2 2 2 4 2 4<br />
a a a z a z a z a a a<br />
<br />
4 6<br />
4 z z<br />
---- + --<br />
2 2<br />
a a</nowiki></pre></td></tr><br />
<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>Kauffman[Link[9, NonAlternating, 28]][a, z]</nowiki></pre></td></tr><br />
<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> 5 10 7 1 2 1 2 2 5 z 7 z<br />
-1 - -- - -- - -- + ----- + ----- + ----- - ---- - ---- + --- + --- + <br />
6 4 2 6 2 4 2 2 2 5 3 5 3<br />
a a a a z a z a z a z a z a a<br />
<br />
2 2 2 3 3 3<br />
3 z 2 6 z 18 z 17 z 3 z 8 z 7 z<br />
--- + a z + 5 z + ---- + ----- + ----- - ---- - ---- - ---- - <br />
a 6 4 2 5 3 a<br />
a a a a a<br />
<br />
4 4 5 5 5 6<br />
3 4 13 z 21 z 3 z z z 5 6 5 z<br />
2 a z - 8 z - ----- - ----- + ---- + -- - -- + a z + 3 z + ---- + <br />
4 2 5 3 a 4<br />
a a a a a<br />
<br />
6 7 7<br />
8 z 2 z 2 z<br />
---- + ---- + ----<br />
2 3 a<br />
a a</nowiki></pre></td></tr><br />
<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>Kh[Link[9, NonAlternating, 28]][q, t]</nowiki></pre></td></tr><br />
<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> 3 1 2 1 2 2 q 3 5<br />
4 q + 4 q + ----- + ----- + ---- + --- + --- + 3 q t + 2 q t + <br />
5 3 3 2 2 q t t<br />
q t q t q t<br />
<br />
5 2 7 2 7 3 9 3 9 4 11 4<br />
3 q t + 3 q t + q t + 3 q t + 2 q t + 3 q t</nowiki></pre></td></tr><br />
</table> }}</div>
BascoBocno
https://katlas.org/index.php?title=L9n28&diff=1693760
L9n28
2009-05-22T19:13:27Z
<p>BascoBocno: </p>
<hr />
<div>http://www.textdompasrold.com <br />
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<!-- <math>\text{Null}</math> --><br />
{{Link Page|<br />
n = 9 |<br />
t = n |<br />
k = 28 |<br />
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,5,-3:8,6,-7,-4:-6,-1,2,-5,4,-8,9,-2,3,7/goTop.html |<br />
braid_table = <table cellspacing=0 cellpadding=0 border=0 style="white-space: pre"><br />
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]]</td></tr><br />
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]]</td></tr><br />
</table> |<br />
khovanov_table = <table border=1><br />
<tr align=center><br />
<td width=16.6667%><table cellpadding=0 cellspacing=0><br />
<tr><td>\</td><td>&nbsp;</td><td>r</td></tr><br />
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr><br />
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr><br />
</table></td><br />
<td width=8.33333%>-3</td ><td width=8.33333%>-2</td ><td width=8.33333%>-1</td ><td width=8.33333%>0</td ><td width=8.33333%>1</td ><td width=8.33333%>2</td ><td width=8.33333%>3</td ><td width=8.33333%>4</td ><td width=16.6667%>&chi;</td></tr><br />
<tr align=center><td>11</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td>3</td></tr><br />
<tr align=center><td>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>2</td><td>-1</td></tr><br />
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>-1</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr><br />
<tr align=center><td>-3</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr><br />
<tr align=center><td>-5</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>-1</td></tr><br />
</table> |<br />
computer_talk =<br />
<table><br />
<tr valign=top><br />
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td><br />
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td><br />
</tr><br />
<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 3, 2005, 2:11:43)...</td></tr><br />
<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[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>9</nowiki></pre></td></tr><br />
<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>Length[Skeleton[Link[9, NonAlternating, 28]]]</nowiki></pre></td></tr><br />
<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>3</nowiki></pre></td></tr><br />
<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>PD[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>PD[X[6, 1, 7, 2], X[12, 7, 13, 8], X[4, 13, 1, 14], X[18, 10, 15, 9], <br />
<br />
X[8, 4, 9, 3], X[5, 17, 6, 16], X[17, 5, 18, 14], X[10, 16, 11, 15], <br />
<br />
X[2, 12, 3, 11]]</nowiki></pre></td></tr><br />
<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>GaussCode[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>GaussCode[{1, -9, 5, -3}, {8, 6, -7, -4}, <br />
<br />
{-6, -1, 2, -5, 4, -8, 9, -2, 3, 7}]</nowiki></pre></td></tr><br />
<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>BR[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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>BR[4, {1, 2, 3, 3, 2, -1, -2, 3, -2, 3, -2}]</nowiki></pre></td></tr><br />
<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>Show[DrawMorseLink[Link[9, NonAlternating, 28]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L9n28_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[7]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr><br />
<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>KnotSignature[Link[9, NonAlternating, 28]]</nowiki></pre></td></tr><br />
<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</nowiki></pre></td></tr><br />
<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>J=Jones[Link[9, NonAlternating, 28]][q]</nowiki></pre></td></tr><br />
<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> -2 3 2 3 4 5<br />
-4 - q + - + 6 q - 5 q + 6 q - 4 q + 3 q<br />
q</nowiki></pre></td></tr><br />
<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>A2Invariant[Link[9, NonAlternating, 28]][q]</nowiki></pre></td></tr><br />
<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> -6 -4 2 6 8 10 12 14 16<br />
1 - q + q + 2 q + 4 q + 2 q + 5 q + 4 q + 3 q + 4 q + <br />
<br />
18 20<br />
q + q</nowiki></pre></td></tr><br />
<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>HOMFLYPT[Link[9, NonAlternating, 28]][a, z]</nowiki></pre></td></tr><br />
<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 2 4<br />
-6 4 3 1 2 1 2 3 z 5 z 4 z<br />
a - -- + -- + ----- - ----- + ----- - 2 z - ---- + ---- - z - -- + <br />
4 2 6 2 4 2 2 2 4 2 4<br />
a a a z a z a z a a a<br />
<br />
4 6<br />
4 z z<br />
---- + --<br />
2 2<br />
a a</nowiki></pre></td></tr><br />
<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>Kauffman[Link[9, NonAlternating, 28]][a, z]</nowiki></pre></td></tr><br />
<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> 5 10 7 1 2 1 2 2 5 z 7 z<br />
-1 - -- - -- - -- + ----- + ----- + ----- - ---- - ---- + --- + --- + <br />
6 4 2 6 2 4 2 2 2 5 3 5 3<br />
a a a a z a z a z a z a z a a<br />
<br />
2 2 2 3 3 3<br />
3 z 2 6 z 18 z 17 z 3 z 8 z 7 z<br />
--- + a z + 5 z + ---- + ----- + ----- - ---- - ---- - ---- - <br />
a 6 4 2 5 3 a<br />
a a a a a<br />
<br />
4 4 5 5 5 6<br />
3 4 13 z 21 z 3 z z z 5 6 5 z<br />
2 a z - 8 z - ----- - ----- + ---- + -- - -- + a z + 3 z + ---- + <br />
4 2 5 3 a 4<br />
a a a a a<br />
<br />
6 7 7<br />
8 z 2 z 2 z<br />
---- + ---- + ----<br />
2 3 a<br />
a a</nowiki></pre></td></tr><br />
<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>Kh[Link[9, NonAlternating, 28]][q, t]</nowiki></pre></td></tr><br />
<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> 3 1 2 1 2 2 q 3 5<br />
4 q + 4 q + ----- + ----- + ---- + --- + --- + 3 q t + 2 q t + <br />
5 3 3 2 2 q t t<br />
q t q t q t<br />
<br />
5 2 7 2 7 3 9 3 9 4 11 4<br />
3 q t + 3 q t + q t + 3 q t + 2 q t + 3 q t</nowiki></pre></td></tr><br />
</table> }}</div>
BascoBocno