DrorsRobot at 06:43, 3 September 2005

2005-09-03T06:43:28Z

← Older revision		Revision as of 02:43, 3 September 2005
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	k = 161 \|		k = 161 \|
	KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-6,2,-1,3,-10,4,-7,5,-2,6,-5,7,-4,8,-11,9,-3,10,-8,11,-9/goTop.html \|		KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-6,2,-1,3,-10,4,-7,5,-2,6,-5,7,-4,8,-11,9,-3,10,-8,11,-9/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:BraidPart3.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:BraidPart3.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:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.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:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.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[Knot[11, Alternating, 161]]</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[Knot[11, Alternating, 161]]</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 21:03, 2 September 2005

2005-09-02T21:03:56Z

Show changes

ScottTestRobot at 21:13, 1 September 2005

2005-09-01T21:13:42Z

Show changes

ScottKnotPageRobot at 16:53, 30 August 2005

2005-08-30T16:53:33Z

New page

{{Hoste-Thistlethwaite Knot Page|
n = 11 |
t = a |
k = 161 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-6,2,-1,3,-10,4,-7,5,-2,6,-5,7,-4,8,-11,9,-3,10,-8,11,-9/goTop.html |
same_alexander = [[10_14]], [[K11n2]], |
same_jones = |
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>5</td><td> </td><td> </td><td> </td><td> </td><td> </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> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow> </td><td>-1</td></tr>
<tr align=center><td>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td> </td><td>2</td></tr>
<tr align=center><td>-1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td> </td><td> </td><td>-2</td></tr>
<tr align=center><td>-3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>4</td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>-5</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>5</td><td bgcolor=yellow>4</td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>-7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>4</td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>-9</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>5</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr>
<tr align=center><td>-11</td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>4</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>-13</td><td> </td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>3</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>-15</td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>3</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>-17</td><td bgcolor=yellow> </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>1</td></tr>
<tr align=center><td>-19</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> |
coloured_jones_2 = |
coloured_jones_3 = |
coloured_jones_4 = |
coloured_jones_5 = |
coloured_jones_6 = |
coloured_jones_7 = |
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[Knot[11, Alternating, 161]]</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>PD[Knot[11, Alternating, 161]]</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>PD[X[4, 2, 5, 1], X[10, 3, 11, 4], X[18, 5, 19, 6], X[14, 8, 15, 7],

X[12, 10, 13, 9], X[2, 11, 3, 12], X[8, 14, 9, 13],

X[20, 15, 21, 16], X[22, 17, 1, 18], X[6, 19, 7, 20],

X[16, 21, 17, 22]]</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>GaussCode[Knot[11, Alternating, 161]]</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>GaussCode[1, -6, 2, -1, 3, -10, 4, -7, 5, -2, 6, -5, 7, -4, 8, -11, 9,

-3, 10, -8, 11, -9]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>BR[Knot[11, Alternating, 161]]</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>BR[Knot[11, Alternating, 161]]</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>Show[DrawMorseLink[Knot[11, Alternating, 161]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:K11a161_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, Alternating, 161]][t]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 8 12 2 3
13 - -- + -- - -- - 12 t + 8 t - 2 t
3 2 t
t t</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Knot[11, Alternating, 161]][z]</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> 2 4 6
1 + 2 z - 4 z - 2 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>
<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>{Knot[10, 14], Knot[11, Alternating, 161], Knot[11, NonAlternating, 2]}</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, Alternating, 161]], KnotSignature[Knot[11, Alternating, 161]]}</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>{57, -4}</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>J=Jones[Knot[11, Alternating, 161]][q]</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> -9 2 4 6 7 9 8 7 6 2
4 - q + -- - -- + -- - -- + -- - -- + -- - - - 2 q + q
8 7 6 5 4 3 2 q
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[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>
<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>{Knot[11, Alternating, 161]}</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[Knot[11, Alternating, 161]][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> -28 -26 -22 -20 -18 -16 3 -10 -8 2
1 - q - q - q + q + q + q + --- + q - q - -- -
14 6
q q

-2 2 6
q + 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>Kauffman[Knot[11, Alternating, 161]][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> 2 4 6 8 3 5 7 9
2 + 3 a + a - 3 a - 2 a + 3 a z + 5 a z + 2 a z + 2 a z + a z -

11 2 2 2 4 2 6 2 8 2 10 2
a z - 9 z - 20 a z - 13 a z + 4 a z + 5 a z - a z -

3 3 3 5 3 7 3 9 3 11 3 4
12 a z - 16 a z - 2 a z - a z - 2 a z + a z + 12 z +

2 4 4 4 6 4 8 4 10 4 5
32 a z + 29 a z + a z - 6 a z + 2 a z + 19 a z +

3 5 5 5 7 5 9 5 6 2 6 4 6
31 a z + 3 a z - 6 a z + 3 a z - 6 z - 14 a z - 21 a z -

6 6 8 6 7 3 7 5 7 7 7 8
9 a z + 4 a z - 11 a z - 23 a z - 8 a z + 4 a z + z -

2 8 4 8 6 8 9 3 9 5 9 2 10
a z + 2 a z + 4 a z + 2 a z + 5 a z + 3 a z + a z +

4 10
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>{Vassiliev[2][Knot[11, Alternating, 161]], Vassiliev[3][Knot[11, Alternating, 161]]}</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>{2, -7}</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, Alternating, 161]][q, t]</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>4 4 1 1 1 3 1 3
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ +
5 3 19 7 17 6 15 6 15 5 13 5 13 4
q q q t q t q t q t q t q t

3 4 3 5 4 3 5 3 t 3 t
------ + ------ + ----- + ----- + ----- + ---- + ---- + --- + --- +
11 4 11 3 9 3 9 2 7 2 7 5 3 q
q t q t q t q t q t q t q t q

2
t 2 3 3 3 5 4
-- + 3 q t + q t + q t + q t
q</nowiki></pre></td></tr>
</table> }}

K11a161 - Revision history

DrorsRobot at 06:43, 3 September 2005

DrorsRobot at 21:03, 2 September 2005

ScottTestRobot at 21:13, 1 September 2005

ScottKnotPageRobot at 16:53, 30 August 2005