ScottTestRobot at 21:57, 1 September 2005

2005-09-01T21:57:51Z

DrorsRobot at 22:41, 31 August 2005

2005-08-31T22:41:25Z

← Older revision		Revision as of 18:41, 31 August 2005
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	{{Rolfsen Knot Page\|		{{Rolfsen Knot Page\|
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	coloured_jones_3 = <math>-q^{30}+2 q^{29}-q^{27}-3 q^{26}+5 q^{25}+q^{24}-6 q^{23}-4 q^{22}+15 q^{21}+4 q^{20}-23 q^{19}-14 q^{18}+41 q^{17}+27 q^{16}-56 q^{15}-53 q^{14}+67 q^{13}+92 q^{12}-79 q^{11}-128 q^{10}+71 q^9+175 q^8-66 q^7-206 q^6+44 q^5+242 q^4-33 q^3-251 q^2+6 q+265+6 q^{-1} -251 q^{-2} -33 q^{-3} +242 q^{-4} +44 q^{-5} -206 q^{-6} -66 q^{-7} +175 q^{-8} +71 q^{-9} -128 q^{-10} -79 q^{-11} +92 q^{-12} +67 q^{-13} -53 q^{-14} -56 q^{-15} +27 q^{-16} +41 q^{-17} -14 q^{-18} -23 q^{-19} +4 q^{-20} +15 q^{-21} -4 q^{-22} -6 q^{-23} + q^{-24} +5 q^{-25} -3 q^{-26} - q^{-27} +2 q^{-29} - q^{-30} </math> \|		coloured_jones_3 = <math>-q^{30}+2 q^{29}-q^{27}-3 q^{26}+5 q^{25}+q^{24}-6 q^{23}-4 q^{22}+15 q^{21}+4 q^{20}-23 q^{19}-14 q^{18}+41 q^{17}+27 q^{16}-56 q^{15}-53 q^{14}+67 q^{13}+92 q^{12}-79 q^{11}-128 q^{10}+71 q^9+175 q^8-66 q^7-206 q^6+44 q^5+242 q^4-33 q^3-251 q^2+6 q+265+6 q^{-1} -251 q^{-2} -33 q^{-3} +242 q^{-4} +44 q^{-5} -206 q^{-6} -66 q^{-7} +175 q^{-8} +71 q^{-9} -128 q^{-10} -79 q^{-11} +92 q^{-12} +67 q^{-13} -53 q^{-14} -56 q^{-15} +27 q^{-16} +41 q^{-17} -14 q^{-18} -23 q^{-19} +4 q^{-20} +15 q^{-21} -4 q^{-22} -6 q^{-23} + q^{-24} +5 q^{-25} -3 q^{-26} - q^{-27} +2 q^{-29} - q^{-30} </math> \|
	coloured_jones_4 = <math>q^{50}-2 q^{49}+q^{47}-q^{46}+6 q^{45}-7 q^{44}+q^{43}+3 q^{42}-9 q^{41}+15 q^{40}-16 q^{39}+9 q^{38}+16 q^{37}-27 q^{36}+19 q^{35}-46 q^{34}+24 q^{33}+63 q^{32}-29 q^{31}+23 q^{30}-140 q^{29}+q^{28}+143 q^{27}+42 q^{26}+97 q^{25}-298 q^{24}-140 q^{23}+166 q^{22}+191 q^{21}+339 q^{20}-423 q^{19}-401 q^{18}+33 q^{17}+315 q^{16}+724 q^{15}-403 q^{14}-657 q^{13}-243 q^{12}+318 q^{11}+1111 q^{10}-256 q^9-803 q^8-528 q^7+220 q^6+1363 q^5-78 q^4-816 q^3-724 q^2+80 q+1447+80 q^{-1} -724 q^{-2} -816 q^{-3} -78 q^{-4} +1363 q^{-5} +220 q^{-6} -528 q^{-7} -803 q^{-8} -256 q^{-9} +1111 q^{-10} +318 q^{-11} -243 q^{-12} -657 q^{-13} -403 q^{-14} +724 q^{-15} +315 q^{-16} +33 q^{-17} -401 q^{-18} -423 q^{-19} +339 q^{-20} +191 q^{-21} +166 q^{-22} -140 q^{-23} -298 q^{-24} +97 q^{-25} +42 q^{-26} +143 q^{-27} + q^{-28} -140 q^{-29} +23 q^{-30} -29 q^{-31} +63 q^{-32} +24 q^{-33} -46 q^{-34} +19 q^{-35} -27 q^{-36} +16 q^{-37} +9 q^{-38} -16 q^{-39} +15 q^{-40} -9 q^{-41} +3 q^{-42} + q^{-43} -7 q^{-44} +6 q^{-45} - q^{-46} + q^{-47} -2 q^{-49} + q^{-50} </math> \|		coloured_jones_4 = <math>q^{50}-2 q^{49}+q^{47}-q^{46}+6 q^{45}-7 q^{44}+q^{43}+3 q^{42}-9 q^{41}+15 q^{40}-16 q^{39}+9 q^{38}+16 q^{37}-27 q^{36}+19 q^{35}-46 q^{34}+24 q^{33}+63 q^{32}-29 q^{31}+23 q^{30}-140 q^{29}+q^{28}+143 q^{27}+42 q^{26}+97 q^{25}-298 q^{24}-140 q^{23}+166 q^{22}+191 q^{21}+339 q^{20}-423 q^{19}-401 q^{18}+33 q^{17}+315 q^{16}+724 q^{15}-403 q^{14}-657 q^{13}-243 q^{12}+318 q^{11}+1111 q^{10}-256 q^9-803 q^8-528 q^7+220 q^6+1363 q^5-78 q^4-816 q^3-724 q^2+80 q+1447+80 q^{-1} -724 q^{-2} -816 q^{-3} -78 q^{-4} +1363 q^{-5} +220 q^{-6} -528 q^{-7} -803 q^{-8} -256 q^{-9} +1111 q^{-10} +318 q^{-11} -243 q^{-12} -657 q^{-13} -403 q^{-14} +724 q^{-15} +315 q^{-16} +33 q^{-17} -401 q^{-18} -423 q^{-19} +339 q^{-20} +191 q^{-21} +166 q^{-22} -140 q^{-23} -298 q^{-24} +97 q^{-25} +42 q^{-26} +143 q^{-27} + q^{-28} -140 q^{-29} +23 q^{-30} -29 q^{-31} +63 q^{-32} +24 q^{-33} -46 q^{-34} +19 q^{-35} -27 q^{-36} +16 q^{-37} +9 q^{-38} -16 q^{-39} +15 q^{-40} -9 q^{-41} +3 q^{-42} + q^{-43} -7 q^{-44} +6 q^{-45} - q^{-46} + q^{-47} -2 q^{-49} + q^{-50} </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, 37]]</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, 37]]</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[10, 4, 11, 3], X[12, 8, 13, 7], X[8, 12, 9, 11],		<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[10, 4, 11, 3], X[12, 8, 13, 7], X[8, 12, 9, 11],
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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>5</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>5</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, 37]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_37_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, 37]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_37_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, 37]]&) /@ {~~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, 37]]&) /@ {
			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>{FullyAmphicheiral, 2, 2, 2, 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>{FullyAmphicheiral, 2, 2, 2, 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, 37]][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, 37]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:33, 30 August 2005

2005-08-30T14:33:50Z

Show changes

DrorsRobot at 01:00, 30 August 2005

2005-08-30T01:00:41Z

← Older revision		Revision as of 21:00, 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 21:59, 29 August 2005

2005-08-29T21:59:32Z

Show changes

ScottTestRobot at 00:06, 29 August 2005

2005-08-29T00:06:16Z

← Older revision		Revision as of 20:06, 28 August 2005
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	<span id="top"></span>		<span id="top"></span>
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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=37\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,6,-7,3,-4,10,-2,4,-3,8,-9,5,-6,7,-5,9,-8/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=37\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,6,-7,3,-4,10,-2,4,-3,8,-9,5,-6,7,-5,9,-8/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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	<td width=13.3333%><table cellpadding=0 cellspacing=0>		<td width=13.3333%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>-9</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>1</td></tr>		<tr align=center><td>-9</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>1</td></tr>
	<tr align=center><td>-11</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>-11</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>
	</table>~~</center>~~		</table>}}

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

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

			[[Category:Knot Page]]

ScottTestRobot at 01:44, 28 August 2005

2005-08-28T01:44:54Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:49:50Z

Resetting knot page to basic template.

New page

10 37 - Revision history

ScottTestRobot at 21:57, 1 September 2005

DrorsRobot at 22:41, 31 August 2005

ScottKnotPageRobot at 14:33, 30 August 2005

DrorsRobot at 01:00, 30 August 2005

DrorsRobot at 21:59, 29 August 2005

ScottTestRobot at 00:06, 29 August 2005

ScottTestRobot at 01:44, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.