ScottTestRobot at 22:05, 1 September 2005

2005-09-01T22:05:55Z

DrorsRobot at 22:54, 31 August 2005

2005-08-31T22:54:48Z

← 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>-q^{15}+3 q^{14}-5 q^{12}-4 q^{11}+10 q^{10}+13 q^9-16 q^8-25 q^7+12 q^6+44 q^5-q^4-58 q^3-22 q^2+69 q+46-63 q^{-1} -81 q^{-2} +61 q^{-3} +101 q^{-4} -39 q^{-5} -128 q^{-6} +27 q^{-7} +140 q^{-8} -6 q^{-9} -154 q^{-10} -7 q^{-11} +154 q^{-12} +24 q^{-13} -151 q^{-14} -38 q^{-15} +137 q^{-16} +51 q^{-17} -115 q^{-18} -59 q^{-19} +87 q^{-20} +59 q^{-21} -53 q^{-22} -54 q^{-23} +26 q^{-24} +41 q^{-25} -9 q^{-26} -23 q^{-27} -3 q^{-28} +11 q^{-29} +5 q^{-30} -4 q^{-31} - q^{-32} - q^{-33} + q^{-34} </math> \|		coloured_jones_3 = <math>-q^{15}+3 q^{14}-5 q^{12}-4 q^{11}+10 q^{10}+13 q^9-16 q^8-25 q^7+12 q^6+44 q^5-q^4-58 q^3-22 q^2+69 q+46-63 q^{-1} -81 q^{-2} +61 q^{-3} +101 q^{-4} -39 q^{-5} -128 q^{-6} +27 q^{-7} +140 q^{-8} -6 q^{-9} -154 q^{-10} -7 q^{-11} +154 q^{-12} +24 q^{-13} -151 q^{-14} -38 q^{-15} +137 q^{-16} +51 q^{-17} -115 q^{-18} -59 q^{-19} +87 q^{-20} +59 q^{-21} -53 q^{-22} -54 q^{-23} +26 q^{-24} +41 q^{-25} -9 q^{-26} -23 q^{-27} -3 q^{-28} +11 q^{-29} +5 q^{-30} -4 q^{-31} - q^{-32} - q^{-33} + q^{-34} </math> \|
	coloured_jones_4 = <math>q^{26}-3 q^{25}+5 q^{23}+4 q^{21}-17 q^{20}-6 q^{19}+17 q^{18}+11 q^{17}+31 q^{16}-46 q^{15}-47 q^{14}+5 q^{13}+27 q^{12}+121 q^{11}-25 q^{10}-96 q^9-89 q^8-50 q^7+222 q^6+108 q^5-26 q^4-189 q^3-268 q^2+183 q+253+208 q^{-1} -148 q^{-2} -510 q^{-3} -21 q^{-4} +273 q^{-5} +477 q^{-6} +34 q^{-7} -646 q^{-8} -267 q^{-9} +180 q^{-10} +667 q^{-11} +238 q^{-12} -677 q^{-13} -453 q^{-14} +66 q^{-15} +763 q^{-16} +390 q^{-17} -646 q^{-18} -572 q^{-19} -38 q^{-20} +782 q^{-21} +498 q^{-22} -549 q^{-23} -624 q^{-24} -159 q^{-25} +689 q^{-26} +566 q^{-27} -348 q^{-28} -572 q^{-29} -289 q^{-30} +458 q^{-31} +533 q^{-32} -89 q^{-33} -378 q^{-34} -332 q^{-35} +163 q^{-36} +357 q^{-37} +83 q^{-38} -132 q^{-39} -228 q^{-40} -22 q^{-41} +135 q^{-42} +86 q^{-43} +8 q^{-44} -78 q^{-45} -44 q^{-46} +16 q^{-47} +25 q^{-48} +19 q^{-49} -7 q^{-50} -11 q^{-51} -2 q^{-52} +3 q^{-54} + q^{-55} - q^{-56} </math> \|		coloured_jones_4 = <math>q^{26}-3 q^{25}+5 q^{23}+4 q^{21}-17 q^{20}-6 q^{19}+17 q^{18}+11 q^{17}+31 q^{16}-46 q^{15}-47 q^{14}+5 q^{13}+27 q^{12}+121 q^{11}-25 q^{10}-96 q^9-89 q^8-50 q^7+222 q^6+108 q^5-26 q^4-189 q^3-268 q^2+183 q+253+208 q^{-1} -148 q^{-2} -510 q^{-3} -21 q^{-4} +273 q^{-5} +477 q^{-6} +34 q^{-7} -646 q^{-8} -267 q^{-9} +180 q^{-10} +667 q^{-11} +238 q^{-12} -677 q^{-13} -453 q^{-14} +66 q^{-15} +763 q^{-16} +390 q^{-17} -646 q^{-18} -572 q^{-19} -38 q^{-20} +782 q^{-21} +498 q^{-22} -549 q^{-23} -624 q^{-24} -159 q^{-25} +689 q^{-26} +566 q^{-27} -348 q^{-28} -572 q^{-29} -289 q^{-30} +458 q^{-31} +533 q^{-32} -89 q^{-33} -378 q^{-34} -332 q^{-35} +163 q^{-36} +357 q^{-37} +83 q^{-38} -132 q^{-39} -228 q^{-40} -22 q^{-41} +135 q^{-42} +86 q^{-43} +8 q^{-44} -78 q^{-45} -44 q^{-46} +16 q^{-47} +25 q^{-48} +19 q^{-49} -7 q^{-50} -11 q^{-51} -2 q^{-52} +3 q^{-54} + q^{-55} - q^{-56} </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, 156]]</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, 156]]</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[4, 2, 5, 1], X[12, 4, 13, 3], X[7, 14, 8, 15], X[18, 9, 19, 10],		<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[4, 2, 5, 1], X[12, 4, 13, 3], X[7, 14, 8, 15], X[18, 9, 19, 10],
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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, 156]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_156_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, 156]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_156_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, 156]]&) /@ {~~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, 156]]&) /@ {
			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, 3, 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, 3, 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, 156]][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, 156]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:41, 30 August 2005

2005-08-30T14:41:56Z

Show changes

DrorsRobot at 01:10, 30 August 2005

2005-08-30T01:10:03Z

← Older revision		Revision as of 21:10, 29 August 2005
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			{\| 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 22:26, 29 August 2005

2005-08-29T22:26:56Z

Show changes

ScottTestRobot at 00:16, 29 August 2005

2005-08-29T00:16:33Z

← Older revision		Revision as of 20:16, 28 August 2005
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	<!-- 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=156\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,6,-5,-3,8,4,-7,10,-2,-8,3,9,-6,7,-4,5,-9/goTop.html}}
	{\| align=left
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=156\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,6,-5,-3,8,4,-7,10,-2,-8,3,9,-6,7,-4,5,-9/goTop.html}}
	\|{{:{{PAGENAME}} Quick Notes}}
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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>
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	<tr align=center><td>-11</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>2</td></tr>		<tr align=center><td>-11</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>2</td></tr>
	<tr align=center><td>-13</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>-13</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</nowiki></pre></td></tr>		q t q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:52, 28 August 2005

2005-08-28T01:52:47Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:41Z

Resetting knot page to basic template.

New page

10 156 - 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 01:10, 30 August 2005

DrorsRobot at 22:26, 29 August 2005

ScottTestRobot at 00:16, 29 August 2005

ScottTestRobot at 01:52, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.