ScottTestRobot at 22:05, 1 September 2005

2005-09-01T22:05:37Z

DrorsRobot at 22:54, 31 August 2005

2005-08-31T22:54:21Z

← Older revision		Revision as of 18:54, 31 August 2005
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	{{Rolfsen Knot Page\|		{{Rolfsen Knot Page\|
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	coloured_jones_3 = <math>2 q^{-1} -2 q^{-2} + q^{-3} -2 q^{-4} +7 q^{-5} -5 q^{-6} -6 q^{-7} +3 q^{-8} +18 q^{-9} -10 q^{-10} -25 q^{-11} +6 q^{-12} +43 q^{-13} -9 q^{-14} -50 q^{-15} - q^{-16} +63 q^{-17} +4 q^{-18} -63 q^{-19} -15 q^{-20} +63 q^{-21} +22 q^{-22} -57 q^{-23} -27 q^{-24} +46 q^{-25} +35 q^{-26} -38 q^{-27} -37 q^{-28} +24 q^{-29} +43 q^{-30} -16 q^{-31} -40 q^{-32} + q^{-33} +41 q^{-34} +6 q^{-35} -33 q^{-36} -15 q^{-37} +25 q^{-38} +19 q^{-39} -15 q^{-40} -18 q^{-41} +5 q^{-42} +15 q^{-43} -9 q^{-45} -3 q^{-46} +5 q^{-47} +2 q^{-48} - q^{-49} -2 q^{-50} + q^{-51} </math> \|		coloured_jones_3 = <math>2 q^{-1} -2 q^{-2} + q^{-3} -2 q^{-4} +7 q^{-5} -5 q^{-6} -6 q^{-7} +3 q^{-8} +18 q^{-9} -10 q^{-10} -25 q^{-11} +6 q^{-12} +43 q^{-13} -9 q^{-14} -50 q^{-15} - q^{-16} +63 q^{-17} +4 q^{-18} -63 q^{-19} -15 q^{-20} +63 q^{-21} +22 q^{-22} -57 q^{-23} -27 q^{-24} +46 q^{-25} +35 q^{-26} -38 q^{-27} -37 q^{-28} +24 q^{-29} +43 q^{-30} -16 q^{-31} -40 q^{-32} + q^{-33} +41 q^{-34} +6 q^{-35} -33 q^{-36} -15 q^{-37} +25 q^{-38} +19 q^{-39} -15 q^{-40} -18 q^{-41} +5 q^{-42} +15 q^{-43} -9 q^{-45} -3 q^{-46} +5 q^{-47} +2 q^{-48} - q^{-49} -2 q^{-50} + q^{-51} </math> \|
	coloured_jones_4 = <math>1+ q^{-1} -2 q^{-2} - q^{-3} +4 q^{-4} -2 q^{-5} +2 q^{-6} -7 q^{-7} -4 q^{-8} +22 q^{-9} -5 q^{-11} -37 q^{-12} -17 q^{-13} +73 q^{-14} +34 q^{-15} -11 q^{-16} -108 q^{-17} -72 q^{-18} +132 q^{-19} +115 q^{-20} +21 q^{-21} -184 q^{-22} -170 q^{-23} +150 q^{-24} +192 q^{-25} +92 q^{-26} -207 q^{-27} -256 q^{-28} +119 q^{-29} +211 q^{-30} +154 q^{-31} -174 q^{-32} -282 q^{-33} +76 q^{-34} +172 q^{-35} +181 q^{-36} -117 q^{-37} -262 q^{-38} +39 q^{-39} +112 q^{-40} +186 q^{-41} -57 q^{-42} -222 q^{-43} + q^{-44} +44 q^{-45} +180 q^{-46} +12 q^{-47} -168 q^{-48} -38 q^{-49} -29 q^{-50} +151 q^{-51} +74 q^{-52} -89 q^{-53} -50 q^{-54} -94 q^{-55} +85 q^{-56} +95 q^{-57} -5 q^{-58} -17 q^{-59} -112 q^{-60} +8 q^{-61} +58 q^{-62} +36 q^{-63} +32 q^{-64} -73 q^{-65} -27 q^{-66} +5 q^{-67} +21 q^{-68} +46 q^{-69} -21 q^{-70} -16 q^{-71} -15 q^{-72} -3 q^{-73} +25 q^{-74} -7 q^{-77} -7 q^{-78} +6 q^{-79} + q^{-80} +2 q^{-81} - q^{-82} -2 q^{-83} + q^{-84} </math> \|		coloured_jones_4 = <math>1+ q^{-1} -2 q^{-2} - q^{-3} +4 q^{-4} -2 q^{-5} +2 q^{-6} -7 q^{-7} -4 q^{-8} +22 q^{-9} -5 q^{-11} -37 q^{-12} -17 q^{-13} +73 q^{-14} +34 q^{-15} -11 q^{-16} -108 q^{-17} -72 q^{-18} +132 q^{-19} +115 q^{-20} +21 q^{-21} -184 q^{-22} -170 q^{-23} +150 q^{-24} +192 q^{-25} +92 q^{-26} -207 q^{-27} -256 q^{-28} +119 q^{-29} +211 q^{-30} +154 q^{-31} -174 q^{-32} -282 q^{-33} +76 q^{-34} +172 q^{-35} +181 q^{-36} -117 q^{-37} -262 q^{-38} +39 q^{-39} +112 q^{-40} +186 q^{-41} -57 q^{-42} -222 q^{-43} + q^{-44} +44 q^{-45} +180 q^{-46} +12 q^{-47} -168 q^{-48} -38 q^{-49} -29 q^{-50} +151 q^{-51} +74 q^{-52} -89 q^{-53} -50 q^{-54} -94 q^{-55} +85 q^{-56} +95 q^{-57} -5 q^{-58} -17 q^{-59} -112 q^{-60} +8 q^{-61} +58 q^{-62} +36 q^{-63} +32 q^{-64} -73 q^{-65} -27 q^{-66} +5 q^{-67} +21 q^{-68} +46 q^{-69} -21 q^{-70} -16 q^{-71} -15 q^{-72} -3 q^{-73} +25 q^{-74} -7 q^{-77} -7 q^{-78} +6 q^{-79} + q^{-80} +2 q^{-81} - q^{-82} -2 q^{-83} + q^{-84} </math> \|
	coloured_jones_5 = \|		coloured_jones_5 = <math>\textrm{NotAvailable}(q)</math> \|
	coloured_jones_6 = \|		coloured_jones_6 = <math>\textrm{NotAvailable}(q)</math> \|
	coloured_jones_7 = \|		coloured_jones_7 = <math>\textrm{NotAvailable}(q)</math> \|
	computer_talk =		computer_talk =
	<table>		<table>
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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 August 29, 2005, 15:33:11)...</td></tr>		<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:27:48)...</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>PD[Knot[10, 131]]</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>PD[Knot[10, 131]]</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>PD[X[1, 4, 2, 5], X[3, 8, 4, 9], X[14, 6, 15, 5], X[15, 20, 16, 1],		<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>PD[X[1, 4, 2, 5], X[3, 8, 4, 9], X[14, 6, 15, 5], X[15, 20, 16, 1],
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	<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>4</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>4</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>Show[DrawMorseLink[Knot[10, 131]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_131_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</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>Show[DrawMorseLink[Knot[10, 131]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_131_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</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[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>(#[Knot[10, 131]]&) /@ {~~SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}</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> (#[Knot[10, 131]]&) /@ {
			SymmetryType, UnknottingNumber, ThreeGenus,
			BridgeIndex, SuperBridgeIndex, NakanishiIndex
			}</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>{Reversible, 1, 2, 3, NotAvailable, 1}</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>{Reversible, 1, 2, 3, NotAvailable, 1}</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>alex = Alexander[Knot[10, 131]][t]</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>alex = Alexander[Knot[10, 131]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:41, 30 August 2005

2005-08-30T14:41:38Z

Show changes

DrorsRobot at 01:09, 30 August 2005

2005-08-30T01:09:39Z

← Older revision		Revision as of 21:09, 29 August 2005
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	</table>		</table>

			{\| width=100%
	See/edit the [[Rolfsen_Splice_Template]].		\|align=left\|See/edit the [[Rolfsen_Splice_Template]].

			Back to the [[#top\|top]].
			\|align=right\|{{Knot Navigation Links\|ext=gif}}
			\|}

	[[Category:Knot Page]]		[[Category:Knot Page]]

DrorsRobot at 22:24, 29 August 2005

2005-08-29T22:24:26Z

Show changes

ScottTestRobot at 00:16, 29 August 2005

2005-08-29T00:16:07Z

← Older revision		Revision as of 20:16, 28 August 2005
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			<!-- -->

			<!-- -->
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	<span id="top"></span>		<span id="top"></span>
			<!-- -->

	<!-- this relies on transclusion for next and previous links -->		<!-- this relies on transclusion for next and previous links -->
	{{Knot Navigation Links\|ext=gif}}		{{Knot Navigation Links\|ext=gif}}

		⚫	{{Rolfsen Knot Page Header\|n=10\|k=131\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,3,-9,-10,2,-5,6,-7,8,9,-3,-4,5,-8,7,-6,4/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=131\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,3,-9,-10,2,-5,6,-7,8,9,-3,-4,5,-8,7,-6,4/goTop.html}}
	\|{{:{{PAGENAME}} Quick Notes}}
	\|}

	<br style="clear:both" />		<br style="clear:both" />
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	{{Vassiliev Invariants}}		{{Vassiliev Invariants}}

	~~===[[~~Khovanov Homology~~]]=~~==		{{Khovanov Homology\|table=<table border=1>

	The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with <font class=HLYellow>yellow</font> highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>{{Data:{{PAGENAME}}/Signature}} is the signature of {{PAGENAME}}. Nonzero entries off the critical diagonals (if any exist) are highlighted in <font class=HLRed>red</font>.

	<center><table border=1>
	<tr align=center>		<tr align=center>
	<td width=15.3846%><table cellpadding=0 cellspacing=0>		<td width=15.3846%><table cellpadding=0 cellspacing=0>
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	<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>-1</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>-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>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>1</td></tr>
	</table>~~</center>~~		</table>}}

	{{Computer Talk Header}}		{{Computer Talk Header}}

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	q t q t q t q t q t q t q t q t q t</nowiki></pre></td></tr>		q t q t q t q t q t q t q t q t q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:52, 28 August 2005

2005-08-28T01:52:24Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:16Z

Resetting knot page to basic template.

New page

10 131 - Revision history

ScottTestRobot at 22:05, 1 September 2005

DrorsRobot at 22:54, 31 August 2005

ScottKnotPageRobot at 14:41, 30 August 2005

DrorsRobot at 01:09, 30 August 2005

DrorsRobot at 22:24, 29 August 2005

ScottTestRobot at 00:16, 29 August 2005

ScottTestRobot at 01:52, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.