ScottTestRobot at 21:57, 1 September 2005

2005-09-01T21:57:33Z

DrorsRobot at 22:40, 31 August 2005

2005-08-31T22:40:57Z

← Older revision		Revision as of 18:40, 31 August 2005
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	coloured_jones_3 = <math> q^{-6} -3 q^{-7} +3 q^{-8} +3 q^{-9} -3 q^{-10} -11 q^{-11} +11 q^{-12} +22 q^{-13} -20 q^{-14} -44 q^{-15} +41 q^{-16} +71 q^{-17} -53 q^{-18} -134 q^{-19} +89 q^{-20} +194 q^{-21} -94 q^{-22} -298 q^{-23} +113 q^{-24} +383 q^{-25} -85 q^{-26} -495 q^{-27} +68 q^{-28} +560 q^{-29} -7 q^{-30} -627 q^{-31} -40 q^{-32} +637 q^{-33} +112 q^{-34} -633 q^{-35} -170 q^{-36} +592 q^{-37} +225 q^{-38} -525 q^{-39} -275 q^{-40} +447 q^{-41} +301 q^{-42} -346 q^{-43} -320 q^{-44} +257 q^{-45} +299 q^{-46} -151 q^{-47} -278 q^{-48} +82 q^{-49} +218 q^{-50} -14 q^{-51} -167 q^{-52} -16 q^{-53} +107 q^{-54} +32 q^{-55} -63 q^{-56} -30 q^{-57} +31 q^{-58} +22 q^{-59} -13 q^{-60} -13 q^{-61} +5 q^{-62} +5 q^{-63} -3 q^{-65} + q^{-66} </math> \|		coloured_jones_3 = <math> q^{-6} -3 q^{-7} +3 q^{-8} +3 q^{-9} -3 q^{-10} -11 q^{-11} +11 q^{-12} +22 q^{-13} -20 q^{-14} -44 q^{-15} +41 q^{-16} +71 q^{-17} -53 q^{-18} -134 q^{-19} +89 q^{-20} +194 q^{-21} -94 q^{-22} -298 q^{-23} +113 q^{-24} +383 q^{-25} -85 q^{-26} -495 q^{-27} +68 q^{-28} +560 q^{-29} -7 q^{-30} -627 q^{-31} -40 q^{-32} +637 q^{-33} +112 q^{-34} -633 q^{-35} -170 q^{-36} +592 q^{-37} +225 q^{-38} -525 q^{-39} -275 q^{-40} +447 q^{-41} +301 q^{-42} -346 q^{-43} -320 q^{-44} +257 q^{-45} +299 q^{-46} -151 q^{-47} -278 q^{-48} +82 q^{-49} +218 q^{-50} -14 q^{-51} -167 q^{-52} -16 q^{-53} +107 q^{-54} +32 q^{-55} -63 q^{-56} -30 q^{-57} +31 q^{-58} +22 q^{-59} -13 q^{-60} -13 q^{-61} +5 q^{-62} +5 q^{-63} -3 q^{-65} + q^{-66} </math> \|
	coloured_jones_4 = <math> q^{-8} -3 q^{-9} +3 q^{-10} +3 q^{-11} -7 q^{-12} +5 q^{-13} -11 q^{-14} +16 q^{-15} +14 q^{-16} -37 q^{-17} +15 q^{-18} -29 q^{-19} +61 q^{-20} +44 q^{-21} -131 q^{-22} +11 q^{-23} -45 q^{-24} +212 q^{-25} +127 q^{-26} -367 q^{-27} -111 q^{-28} -88 q^{-29} +603 q^{-30} +428 q^{-31} -749 q^{-32} -554 q^{-33} -339 q^{-34} +1252 q^{-35} +1163 q^{-36} -1034 q^{-37} -1322 q^{-38} -1038 q^{-39} +1854 q^{-40} +2274 q^{-41} -901 q^{-42} -2058 q^{-43} -2104 q^{-44} +2030 q^{-45} +3311 q^{-46} -337 q^{-47} -2342 q^{-48} -3120 q^{-49} +1701 q^{-50} +3841 q^{-51} +372 q^{-52} -2086 q^{-53} -3719 q^{-54} +1064 q^{-55} +3761 q^{-56} +993 q^{-57} -1452 q^{-58} -3839 q^{-59} +304 q^{-60} +3208 q^{-61} +1458 q^{-62} -613 q^{-63} -3538 q^{-64} -470 q^{-65} +2303 q^{-66} +1702 q^{-67} +297 q^{-68} -2834 q^{-69} -1077 q^{-70} +1193 q^{-71} +1567 q^{-72} +1024 q^{-73} -1796 q^{-74} -1244 q^{-75} +172 q^{-76} +1019 q^{-77} +1265 q^{-78} -746 q^{-79} -908 q^{-80} -387 q^{-81} +349 q^{-82} +975 q^{-83} -86 q^{-84} -382 q^{-85} -415 q^{-86} -60 q^{-87} +492 q^{-88} +98 q^{-89} -44 q^{-90} -208 q^{-91} -135 q^{-92} +160 q^{-93} +58 q^{-94} +41 q^{-95} -56 q^{-96} -71 q^{-97} +34 q^{-98} +11 q^{-99} +23 q^{-100} -6 q^{-101} -20 q^{-102} +5 q^{-103} +5 q^{-105} -3 q^{-107} + q^{-108} </math> \|		coloured_jones_4 = <math> q^{-8} -3 q^{-9} +3 q^{-10} +3 q^{-11} -7 q^{-12} +5 q^{-13} -11 q^{-14} +16 q^{-15} +14 q^{-16} -37 q^{-17} +15 q^{-18} -29 q^{-19} +61 q^{-20} +44 q^{-21} -131 q^{-22} +11 q^{-23} -45 q^{-24} +212 q^{-25} +127 q^{-26} -367 q^{-27} -111 q^{-28} -88 q^{-29} +603 q^{-30} +428 q^{-31} -749 q^{-32} -554 q^{-33} -339 q^{-34} +1252 q^{-35} +1163 q^{-36} -1034 q^{-37} -1322 q^{-38} -1038 q^{-39} +1854 q^{-40} +2274 q^{-41} -901 q^{-42} -2058 q^{-43} -2104 q^{-44} +2030 q^{-45} +3311 q^{-46} -337 q^{-47} -2342 q^{-48} -3120 q^{-49} +1701 q^{-50} +3841 q^{-51} +372 q^{-52} -2086 q^{-53} -3719 q^{-54} +1064 q^{-55} +3761 q^{-56} +993 q^{-57} -1452 q^{-58} -3839 q^{-59} +304 q^{-60} +3208 q^{-61} +1458 q^{-62} -613 q^{-63} -3538 q^{-64} -470 q^{-65} +2303 q^{-66} +1702 q^{-67} +297 q^{-68} -2834 q^{-69} -1077 q^{-70} +1193 q^{-71} +1567 q^{-72} +1024 q^{-73} -1796 q^{-74} -1244 q^{-75} +172 q^{-76} +1019 q^{-77} +1265 q^{-78} -746 q^{-79} -908 q^{-80} -387 q^{-81} +349 q^{-82} +975 q^{-83} -86 q^{-84} -382 q^{-85} -415 q^{-86} -60 q^{-87} +492 q^{-88} +98 q^{-89} -44 q^{-90} -208 q^{-91} -135 q^{-92} +160 q^{-93} +58 q^{-94} +41 q^{-95} -56 q^{-96} -71 q^{-97} +34 q^{-98} +11 q^{-99} +23 q^{-100} -6 q^{-101} -20 q^{-102} +5 q^{-103} +5 q^{-105} -3 q^{-107} + q^{-108} </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, 53]]</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, 53]]</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[5, 14, 6, 15], 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[5, 14, 6, 15], 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>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, 53]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_53_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, 53]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_53_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, 53]]&) /@ {~~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, 53]]&) /@ {
			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, {2, 3}, 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, {2, 3}, 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, 53]][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, 53]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:33, 30 August 2005

2005-08-30T14:33:32Z

Show changes

DrorsRobot at 01:00, 30 August 2005

2005-08-30T01:00:20Z

← 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 21:58, 29 August 2005

2005-08-29T21:58:42Z

Show changes

ScottTestRobot at 00:05, 29 August 2005

2005-08-29T00:05:52Z

← Older revision		Revision as of 20:05, 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=53\|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
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=53\|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}}
	\|}

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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>-23</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> </td><td> </td><td>-2</td></tr>		<tr align=center><td>-23</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> </td><td> </td><td>-2</td></tr>
	<tr align=center><td>-25</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>-25</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 q t q t</nowiki></pre></td></tr>		q t q t q t q t q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:44, 28 August 2005

2005-08-28T01:44:40Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:05Z

Resetting knot page to basic template.

New page

10 53 - Revision history

ScottTestRobot at 21:57, 1 September 2005

DrorsRobot at 22:40, 31 August 2005

ScottKnotPageRobot at 14:33, 30 August 2005

DrorsRobot at 01:00, 30 August 2005

DrorsRobot at 21:58, 29 August 2005

ScottTestRobot at 00:05, 29 August 2005

ScottTestRobot at 01:44, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.