DrorsRobot at 07:57, 3 September 2005

2005-09-03T07:57:50Z

← Older revision		Revision as of 02:57, 3 September 2005
Line 16:		Line 16:
	k = 411 \|		k = 411 \|
	KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:-5,4,-9,3:10,-1,-4,8,-6,5,11,-2,-3,7,-8,6,-7,9/goTop.html \|		KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:-5,4,-9,3:10,-1,-4,8,-6,5,11,-2,-3,7,-8,6,-7,9/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:BraidPart3.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]]</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:BraidPart3.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]]</td></tr>
	<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]]</td></tr>		<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]]</td></tr>
Line 51:		Line 51:
	<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, 411]]</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, 411]]</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 23:27, 2 September 2005

2005-09-02T23:27:16Z

Show changes

DrorsRobot at 17:21, 31 August 2005

2005-08-31T17:21:09Z

Show changes

ScottKnotPageRobot at 17:42, 30 August 2005

2005-08-30T17:42:43Z

New page

{{Link Page|
n = 11 |
t = n |
k = 411 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:-5,4,-9,3:10,-1,-4,8,-6,5,11,-2,-3,7,-8,6,-7,9/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%>-11</td ><td width=6.25%>-10</td ><td width=6.25%>-9</td ><td width=6.25%>-8</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=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=red>1</td><td>1</td></tr>
<tr align=center><td>-7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=red>1</td><td>0</td></tr>
<tr align=center><td>-9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=red>2</td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>-11</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=red>1</td><td bgcolor=red>1</td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>-13</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>2</td><td bgcolor=red>5</td><td bgcolor=red>2</td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>-15</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>2</td><td bgcolor=red>2</td><td bgcolor=red>3</td><td> </td><td> </td><td> </td><td> </td><td>3</td></tr>
<tr align=center><td>-17</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>2</td><td bgcolor=red>5</td><td bgcolor=red>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>-19</td><td> </td><td> </td><td> </td><td bgcolor=red>2</td><td bgcolor=red>2</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>-21</td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=red>3</td><td bgcolor=red>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>-23</td><td> </td><td bgcolor=red>1</td><td bgcolor=red>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
<tr align=center><td>-25</td><td> </td><td bgcolor=red>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>-27</td><td bgcolor=red>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, 411]]</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, 411]]]</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>3</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, 411]]</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[13, 22, 14, 19], X[7, 20, 8, 21],

X[19, 10, 20, 11], X[9, 16, 10, 17], X[17, 14, 18, 15],

X[15, 8, 16, 9], X[21, 18, 22, 5], 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, 411]]</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}, {-5, 4, -9, 3},

{10, -1, -4, 8, -6, 5, 11, -2, -3, 7, -8, 6, -7, 9}]</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, 411]]</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, 411]]</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, 411]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11n411_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, 411]][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, 411]][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, 411]], KnotSignature[Link[11, NonAlternating, 411]]}</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, -5}</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, 411]][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> -13 2 2 -10 -8 2 -6 2 -4 -3
-q + --- - --- + q + q + -- - q + -- - q + q
12 11 7 5
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, 411]][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> -42 3 -38 -36 3 3 6 5 6 4 -20
-q - --- - q - q + --- + --- + --- + --- + --- + --- + q +
40 32 30 28 26 24 22
q q q q q q q

2 -16 -14 -10
--- + q + q + q
18
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, 411]][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> 8 10 12 14
6 8 10 12 2 a 5 a 4 a a 6 2
2 a + 5 a - 12 a + 5 a + ---- - ----- + ----- - --- + 6 a z +
2 2 2 2
z z z z

8 2 10 2 6 4 8 4 10 4 6 6 8 6
6 a z - 8 a z + 5 a z + 5 a z - a z + a z + 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, 411]][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> 8 10 12 14
6 8 10 12 14 2 a 5 a 4 a a
-2 a + 7 a + 21 a + 16 a + 3 a - ---- - ----- - ----- - --- +
2 2 2 2
z z z z

9 11 13 15
5 a 9 a 5 a a 9 11 13
---- + ----- + ----- + --- - 22 a z - 39 a z - 21 a z -
z z z z

15 6 2 8 2 10 2 12 2 14 2
4 a z + 6 a z - 10 a z - 43 a z - 35 a z - 8 a z +

7 3 9 3 11 3 13 3 15 3 6 4
2 a z + 32 a z + 54 a z + 30 a z + 6 a z - 5 a z +

8 4 10 4 12 4 14 4 7 5 9 5
7 a z + 44 a z + 47 a z + 15 a z - 4 a z - 19 a z -

11 5 13 5 15 5 6 6 8 6 10 6
20 a z - 10 a z - 5 a z + a z - 5 a z - 21 a z -

12 6 14 6 7 7 9 7 11 7 13 7
26 a z - 11 a z + a z + 3 a z - 2 a z - 3 a z +

15 7 8 8 10 8 12 8 14 8 11 9 13 9
a z + a z + 3 a z + 4 a z + 2 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, 411]], Vassiliev[3][Link[11, NonAlternating, 411]]}</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> 64
{0, --}
3</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, 411]][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> -7 -5 1 1 1 1 1 3
q + q + ------- + ------- + ------- + ------ + ------ + ------ +
27 11 25 10 23 10 23 9 21 9 21 8
q t q t q t q t q t q t

2 3 2 2 1 5 2
------ + ------ + ------ + ------ + ------ + ------ + ------ +
19 8 21 7 19 7 17 7 19 6 17 6 15 6
q t q t q t q t q t q t q t

2 2 2 3 5 1 2
------ + ------ + ------ + ------ + ------ + ------ + ------ +
17 5 15 5 13 5 15 4 13 4 11 4 13 3
q t q t q t q t q t q t q t

1 1 1 2 1
------ + ----- + ------ + ----- + ----
11 3 9 3 11 2 9 2 7
q t q t q t q t q t</nowiki></pre></td></tr>
</table> }}

L11n411 - Revision history

DrorsRobot at 07:57, 3 September 2005

DrorsRobot at 23:27, 2 September 2005

DrorsRobot at 17:21, 31 August 2005

ScottKnotPageRobot at 17:42, 30 August 2005