ScottTestRobot at 21:59, 1 September 2005

2005-09-01T21:59:03Z

DrorsRobot at 22:43, 31 August 2005

2005-08-31T22:43:10Z

← Older revision		Revision as of 18:43, 31 August 2005
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	coloured_jones_3 = <math> q^{-6} -2 q^{-7} + q^{-8} + q^{-9} +3 q^{-10} -6 q^{-11} + q^{-12} +4 q^{-13} +2 q^{-14} -9 q^{-15} +10 q^{-16} +5 q^{-17} -16 q^{-18} -20 q^{-19} +51 q^{-20} +23 q^{-21} -73 q^{-22} -61 q^{-23} +118 q^{-24} +92 q^{-25} -140 q^{-26} -153 q^{-27} +169 q^{-28} +193 q^{-29} -160 q^{-30} -250 q^{-31} +156 q^{-32} +277 q^{-33} -125 q^{-34} -298 q^{-35} +90 q^{-36} +302 q^{-37} -50 q^{-38} -289 q^{-39} +275 q^{-41} +38 q^{-42} -236 q^{-43} -85 q^{-44} +201 q^{-45} +110 q^{-46} -145 q^{-47} -134 q^{-48} +100 q^{-49} +126 q^{-50} -46 q^{-51} -114 q^{-52} +11 q^{-53} +86 q^{-54} +12 q^{-55} -56 q^{-56} -20 q^{-57} +30 q^{-58} +19 q^{-59} -14 q^{-60} -12 q^{-61} +5 q^{-62} +5 q^{-63} -3 q^{-65} + q^{-66} </math> \|		coloured_jones_3 = <math> q^{-6} -2 q^{-7} + q^{-8} + q^{-9} +3 q^{-10} -6 q^{-11} + q^{-12} +4 q^{-13} +2 q^{-14} -9 q^{-15} +10 q^{-16} +5 q^{-17} -16 q^{-18} -20 q^{-19} +51 q^{-20} +23 q^{-21} -73 q^{-22} -61 q^{-23} +118 q^{-24} +92 q^{-25} -140 q^{-26} -153 q^{-27} +169 q^{-28} +193 q^{-29} -160 q^{-30} -250 q^{-31} +156 q^{-32} +277 q^{-33} -125 q^{-34} -298 q^{-35} +90 q^{-36} +302 q^{-37} -50 q^{-38} -289 q^{-39} +275 q^{-41} +38 q^{-42} -236 q^{-43} -85 q^{-44} +201 q^{-45} +110 q^{-46} -145 q^{-47} -134 q^{-48} +100 q^{-49} +126 q^{-50} -46 q^{-51} -114 q^{-52} +11 q^{-53} +86 q^{-54} +12 q^{-55} -56 q^{-56} -20 q^{-57} +30 q^{-58} +19 q^{-59} -14 q^{-60} -12 q^{-61} +5 q^{-62} +5 q^{-63} -3 q^{-65} + q^{-66} </math> \|
	coloured_jones_4 = <math> q^{-8} -2 q^{-9} + q^{-10} + q^{-11} - q^{-12} +6 q^{-13} -10 q^{-14} +2 q^{-15} +3 q^{-16} -4 q^{-17} +25 q^{-18} -24 q^{-19} -8 q^{-21} -21 q^{-22} +76 q^{-23} -16 q^{-24} +6 q^{-25} -66 q^{-26} -107 q^{-27} +159 q^{-28} +78 q^{-29} +98 q^{-30} -180 q^{-31} -377 q^{-32} +177 q^{-33} +296 q^{-34} +421 q^{-35} -237 q^{-36} -867 q^{-37} -42 q^{-38} +492 q^{-39} +1001 q^{-40} -43 q^{-41} -1379 q^{-42} -514 q^{-43} +446 q^{-44} +1590 q^{-45} +399 q^{-46} -1626 q^{-47} -985 q^{-48} +130 q^{-49} +1891 q^{-50} +862 q^{-51} -1537 q^{-52} -1221 q^{-53} -269 q^{-54} +1845 q^{-55} +1149 q^{-56} -1230 q^{-57} -1198 q^{-58} -618 q^{-59} +1555 q^{-60} +1259 q^{-61} -802 q^{-62} -1005 q^{-63} -905 q^{-64} +1100 q^{-65} +1225 q^{-66} -295 q^{-67} -667 q^{-68} -1093 q^{-69} +527 q^{-70} +1009 q^{-71} +168 q^{-72} -201 q^{-73} -1045 q^{-74} -16 q^{-75} +583 q^{-76} +390 q^{-77} +248 q^{-78} -715 q^{-79} -301 q^{-80} +116 q^{-81} +291 q^{-82} +445 q^{-83} -283 q^{-84} -255 q^{-85} -144 q^{-86} +57 q^{-87} +346 q^{-88} -17 q^{-89} -77 q^{-90} -142 q^{-91} -69 q^{-92} +149 q^{-93} +35 q^{-94} +19 q^{-95} -53 q^{-96} -58 q^{-97} +36 q^{-98} +11 q^{-99} +20 q^{-100} -7 q^{-101} -19 q^{-102} +5 q^{-103} +5 q^{-105} -3 q^{-107} + q^{-108} </math> \|		coloured_jones_4 = <math> q^{-8} -2 q^{-9} + q^{-10} + q^{-11} - q^{-12} +6 q^{-13} -10 q^{-14} +2 q^{-15} +3 q^{-16} -4 q^{-17} +25 q^{-18} -24 q^{-19} -8 q^{-21} -21 q^{-22} +76 q^{-23} -16 q^{-24} +6 q^{-25} -66 q^{-26} -107 q^{-27} +159 q^{-28} +78 q^{-29} +98 q^{-30} -180 q^{-31} -377 q^{-32} +177 q^{-33} +296 q^{-34} +421 q^{-35} -237 q^{-36} -867 q^{-37} -42 q^{-38} +492 q^{-39} +1001 q^{-40} -43 q^{-41} -1379 q^{-42} -514 q^{-43} +446 q^{-44} +1590 q^{-45} +399 q^{-46} -1626 q^{-47} -985 q^{-48} +130 q^{-49} +1891 q^{-50} +862 q^{-51} -1537 q^{-52} -1221 q^{-53} -269 q^{-54} +1845 q^{-55} +1149 q^{-56} -1230 q^{-57} -1198 q^{-58} -618 q^{-59} +1555 q^{-60} +1259 q^{-61} -802 q^{-62} -1005 q^{-63} -905 q^{-64} +1100 q^{-65} +1225 q^{-66} -295 q^{-67} -667 q^{-68} -1093 q^{-69} +527 q^{-70} +1009 q^{-71} +168 q^{-72} -201 q^{-73} -1045 q^{-74} -16 q^{-75} +583 q^{-76} +390 q^{-77} +248 q^{-78} -715 q^{-79} -301 q^{-80} +116 q^{-81} +291 q^{-82} +445 q^{-83} -283 q^{-84} -255 q^{-85} -144 q^{-86} +57 q^{-87} +346 q^{-88} -17 q^{-89} -77 q^{-90} -142 q^{-91} -69 q^{-92} +149 q^{-93} +35 q^{-94} +19 q^{-95} -53 q^{-96} -58 q^{-97} +36 q^{-98} +11 q^{-99} +20 q^{-100} -7 q^{-101} -19 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, 55]]</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, 55]]</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, 12, 6, 13], X[15, 18, 16, 19],		<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, 12, 6, 13], X[15, 18, 16, 19],
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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, 55]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_55_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, 55]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_55_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, 55]]&) /@ {~~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, 55]]&) /@ {
			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, 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, 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, 55]][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, 55]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:34, 30 August 2005

2005-08-30T14:34:56Z

Show changes

DrorsRobot at 01:02, 30 August 2005

2005-08-30T01:02:04Z

← Older revision		Revision as of 21:02, 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 22:02, 29 August 2005

2005-08-29T22:02:50Z

Show changes

ScottTestRobot at 00:07, 29 August 2005

2005-08-29T00:07:43Z

← Older revision		Revision as of 20:07, 28 August 2005
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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=55\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-3,9,-10,2,-5,6,-9,3,-7,8,-4,5,-6,4,-8,7/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=55\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-3,9,-10,2,-5,6,-9,3,-7,8,-4,5,-6,4,-8,7/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>-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 01:45, 28 August 2005

2005-08-28T01:45:45Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:07Z

Resetting knot page to basic template.

New page

10 55 - Revision history

ScottTestRobot at 21:59, 1 September 2005

DrorsRobot at 22:43, 31 August 2005

ScottKnotPageRobot at 14:34, 30 August 2005

DrorsRobot at 01:02, 30 August 2005

DrorsRobot at 22:02, 29 August 2005

ScottTestRobot at 00:07, 29 August 2005

ScottTestRobot at 01:45, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.