DrorsRobot at 07:25, 3 September 2005

2005-09-03T07:25:08Z

← Older revision		Revision as of 03:25, 3 September 2005
Line 16:		Line 16:
	k = 456 \|		k = 456 \|
	KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:-7,4,-6,5:10,-1,-9,8,-4,7:11,-2,-5,6,-3,9,-8,3/goTop.html \|		KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:-7,4,-6,5:10,-1,-9,8,-4,7:11,-2,-5,6,-3,9,-8,3/goTop.html \|
	braid_table = <table cellspacing=0 cellpadding=0 border=0>		braid_table = <table cellspacing=0 cellpadding=0 border=0 style="white-space: pre">
	<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.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]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>		<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.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]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
	<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>		<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
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	<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>		<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>
	</tr>		</tr>
	<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 2, 2005, 15:8:39)...</td></tr>		<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 3, 2005, 2:11:43)...</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>Crossings[Link[11, NonAlternating, 456]]</nowiki></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>Crossings[Link[11, NonAlternating, 456]]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=  </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>Out[2]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>11</nowiki></pre></td></tr>

DrorsRobot at 22:53, 2 September 2005

2005-09-02T22:53:31Z

Show changes

ScottTestRobot at 22:43, 1 September 2005

2005-09-01T22:43:23Z

Show changes

DrorsRobot at 16:55, 31 August 2005

2005-08-31T16:55:42Z

Show changes

ScottKnotPageRobot at 17:22, 30 August 2005

2005-08-30T17:22:23Z

New page

{{Link Page|
n = 11 |
t = n |
k = 456 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:-7,4,-6,5:10,-1,-9,8,-4,7:11,-2,-5,6,-3,9,-8,3/goTop.html |
khovanov_table = <table border=1>
<tr align=center>
<td width=12.5%><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=6.25%>-7</td ><td width=6.25%>-6</td ><td width=6.25%>-5</td ><td width=6.25%>-4</td ><td width=6.25%>-3</td ><td width=6.25%>-2</td ><td width=6.25%>-1</td ><td width=6.25%>0</td ><td width=6.25%>1</td ><td width=6.25%>2</td ><td width=6.25%>3</td ><td width=6.25%>4</td ><td width=12.5%>χ</td></tr>
<tr align=center><td>6</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow>1</td><td>1</td></tr>
<tr align=center><td>4</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td bgcolor=red>1</td><td>1</td></tr>
<tr align=center><td>2</td><td> </td><td> </td><td> </td><td> </td><td> </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>0</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>4</td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td>4</td></tr>
<tr align=center><td>-2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow>4</td><td bgcolor=red>1</td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>-4</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>6</td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>4</td></tr>
<tr align=center><td>-6</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>6</td><td bgcolor=red>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr>
<tr align=center><td>-8</td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>3</td><td bgcolor=red>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>-10</td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow>4</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr>
<tr align=center><td>-12</td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>-14</td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr>
<tr align=center><td>-16</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
</table> |
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>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</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>Crossings[Link[11, NonAlternating, 456]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=  </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>Length[Skeleton[Link[11, NonAlternating, 456]]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>4</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>PD[Link[11, NonAlternating, 456]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[15, 18, 16, 11], X[9, 21, 10, 20],

X[13, 19, 14, 22], X[21, 15, 22, 14], X[19, 5, 20, 10],

X[17, 8, 18, 9], X[7, 16, 8, 17], X[2, 5, 3, 6], X[4, 11, 1, 12]]</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>GaussCode[Link[11, NonAlternating, 456]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[{1, -10, 2, -11}, {-7, 4, -6, 5}, {10, -1, -9, 8, -4, 7},

{11, -2, -5, 6, -3, 9, -8, 3}]</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>BR[Link[11, NonAlternating, 456]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[Link[11, NonAlternating, 456]]</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>Show[DrawMorseLink[Link[11, NonAlternating, 456]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11n456_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>
<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>alex = Alexander[Link[11, NonAlternating, 456]][t]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>ComplexInfinity</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>Conway[Link[11, NonAlternating, 456]][z]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>ComplexInfinity</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>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{}</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>{KnotDet[Link[11, NonAlternating, 456]], KnotSignature[Link[11, NonAlternating, 456]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Infinity, -1}</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>J=Jones[Link[11, NonAlternating, 456]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -(15/2) 3 4 6 5 7 3 4 5/2
q - ----- + ----- - ---- + ---- - ---- + ---- - ------- - q
13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q q</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>A2Invariant[Link[11, NonAlternating, 456]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -24 2 3 3 4 9 10 14 11 9 2
8 - q + --- + --- + --- + --- + --- + -- + -- + -- + -- + 3 q +
20 16 14 12 10 8 6 4 2
q q q q q q q q q

4 6 8
3 q + 2 q + q</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>HOMFLYPT[Link[11, NonAlternating, 456]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 5 3 5
1 3 a 3 a a 3 8 a 7 a 2 a 4 z
-(----) + --- - ---- + -- - --- + --- - ---- + ---- - --- + 11 a z -
3 3 3 3 a z z z z a
a z z z z

3
3 5 7 z 3 3 3 5 3 5
9 a z + 3 a z - a z - -- + 7 a z - 4 a z + 2 a z + a z -
a

3 5
a z</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>Kauffman[Link[11, NonAlternating, 456]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 5 2 4
2 4 1 3 a 3 a a 3 6 a 3 a 5
10 + 19 a + 10 a + ---- + --- + ---- + -- - -- - ---- - ---- - --- -
3 3 3 3 2 2 2 a z
a z z z z z z z

3 5
12 a 12 a 5 a 11 z 3 5 7
---- - ----- - ---- + ---- + 23 a z + 21 a z + 12 a z + 3 a z -
z z z a

3
2 2 2 4 2 6 2 8 2 14 z 3
12 z - 15 a z - 3 a z - a z - a z - ----- - 18 a z -
a

3 3 5 3 7 3 4 2 4 4 4 6 4
17 a z - 22 a z - 9 a z + 4 z - 4 a z - 16 a z - 5 a z +

5
8 4 7 z 5 3 5 5 5 7 5 2 6
3 a z + ---- + 4 a z + 2 a z + 16 a z + 11 a z + 5 a z +
a

7
4 6 6 6 8 6 z 3 7 5 7 7 7
16 a z + 10 a z - a z - -- + 3 a z - a z - 3 a z -
a

2 8 4 8 6 8 3 9 5 9
a z - 4 a z - 3 a z - a z - a z</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>{Vassiliev[2][Link[11, NonAlternating, 456]], Vassiliev[3][Link[11, NonAlternating, 456]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[16]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 47
{0, -(--)}
12</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>Kh[Link[11, NonAlternating, 456]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[17]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 4 1 2 1 2 2 4 3
4 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- +
2 16 7 14 6 12 6 12 5 10 5 10 4 8 4
q q t q t q t q t q t q t q t

3 3 1 6 6 1 2 2 t
----- + ----- + ----- + ----- + ----- + ---- + ---- + ---- + -- +
8 3 6 3 8 2 6 2 4 2 6 4 2 2
q t q t q t q t q t q t q t q t q

2 2 2 4 4 6 4
q t + q t + q t + q t</nowiki></pre></td></tr>
</table> }}

L11n456 - Revision history

DrorsRobot at 07:25, 3 September 2005

DrorsRobot at 22:53, 2 September 2005

ScottTestRobot at 22:43, 1 September 2005

DrorsRobot at 16:55, 31 August 2005

ScottKnotPageRobot at 17:22, 30 August 2005