ScottTestRobot at 22:03, 1 September 2005

2005-09-01T22:03:15Z

DrorsRobot at 22:50, 31 August 2005

2005-08-31T22:50:06Z

← Older revision		Revision as of 18:50, 31 August 2005
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	coloured_jones_3 = <math>q^9-2 q^8+q^7+q^6+2 q^5-7 q^4+2 q^3+7 q^2+q-17+8 q^{-1} +18 q^{-2} -8 q^{-3} -36 q^{-4} +30 q^{-5} +42 q^{-6} -40 q^{-7} -72 q^{-8} +70 q^{-9} +97 q^{-10} -87 q^{-11} -138 q^{-12} +105 q^{-13} +175 q^{-14} -106 q^{-15} -214 q^{-16} +99 q^{-17} +240 q^{-18} -80 q^{-19} -252 q^{-20} +50 q^{-21} +256 q^{-22} -21 q^{-23} -245 q^{-24} -13 q^{-25} +227 q^{-26} +44 q^{-27} -201 q^{-28} -72 q^{-29} +169 q^{-30} +95 q^{-31} -132 q^{-32} -107 q^{-33} +92 q^{-34} +107 q^{-35} -52 q^{-36} -98 q^{-37} +20 q^{-38} +78 q^{-39} +2 q^{-40} -53 q^{-41} -14 q^{-42} +31 q^{-43} +16 q^{-44} -15 q^{-45} -11 q^{-46} +5 q^{-47} +5 q^{-48} -3 q^{-50} + q^{-51} </math> \|		coloured_jones_3 = <math>q^9-2 q^8+q^7+q^6+2 q^5-7 q^4+2 q^3+7 q^2+q-17+8 q^{-1} +18 q^{-2} -8 q^{-3} -36 q^{-4} +30 q^{-5} +42 q^{-6} -40 q^{-7} -72 q^{-8} +70 q^{-9} +97 q^{-10} -87 q^{-11} -138 q^{-12} +105 q^{-13} +175 q^{-14} -106 q^{-15} -214 q^{-16} +99 q^{-17} +240 q^{-18} -80 q^{-19} -252 q^{-20} +50 q^{-21} +256 q^{-22} -21 q^{-23} -245 q^{-24} -13 q^{-25} +227 q^{-26} +44 q^{-27} -201 q^{-28} -72 q^{-29} +169 q^{-30} +95 q^{-31} -132 q^{-32} -107 q^{-33} +92 q^{-34} +107 q^{-35} -52 q^{-36} -98 q^{-37} +20 q^{-38} +78 q^{-39} +2 q^{-40} -53 q^{-41} -14 q^{-42} +31 q^{-43} +16 q^{-44} -15 q^{-45} -11 q^{-46} +5 q^{-47} +5 q^{-48} -3 q^{-50} + q^{-51} </math> \|
	coloured_jones_4 = <math>q^{16}-2 q^{15}+q^{14}+q^{13}-2 q^{12}+5 q^{11}-9 q^{10}+4 q^9+5 q^8-8 q^7+17 q^6-25 q^5+10 q^4+10 q^3-26 q^2+45 q-40+27 q^{-1} -84 q^{-3} +93 q^{-4} -24 q^{-5} +91 q^{-6} -33 q^{-7} -241 q^{-8} +117 q^{-9} +55 q^{-10} +279 q^{-11} -47 q^{-12} -536 q^{-13} +23 q^{-14} +151 q^{-15} +627 q^{-16} +59 q^{-17} -883 q^{-18} -231 q^{-19} +136 q^{-20} +1018 q^{-21} +324 q^{-22} -1092 q^{-23} -528 q^{-24} -57 q^{-25} +1253 q^{-26} +633 q^{-27} -1067 q^{-28} -694 q^{-29} -327 q^{-30} +1243 q^{-31} +830 q^{-32} -864 q^{-33} -676 q^{-34} -564 q^{-35} +1046 q^{-36} +893 q^{-37} -576 q^{-38} -546 q^{-39} -735 q^{-40} +745 q^{-41} +855 q^{-42} -246 q^{-43} -342 q^{-44} -835 q^{-45} +378 q^{-46} +716 q^{-47} +69 q^{-48} -74 q^{-49} -804 q^{-50} +19 q^{-51} +452 q^{-52} +254 q^{-53} +199 q^{-54} -597 q^{-55} -202 q^{-56} +136 q^{-57} +231 q^{-58} +346 q^{-59} -289 q^{-60} -210 q^{-61} -81 q^{-62} +79 q^{-63} +299 q^{-64} -56 q^{-65} -89 q^{-66} -115 q^{-67} -38 q^{-68} +148 q^{-69} +22 q^{-70} +4 q^{-71} -54 q^{-72} -49 q^{-73} +40 q^{-74} +11 q^{-75} +17 q^{-76} -8 q^{-77} -18 q^{-78} +5 q^{-79} +5 q^{-81} -3 q^{-83} + q^{-84} </math> \|		coloured_jones_4 = <math>q^{16}-2 q^{15}+q^{14}+q^{13}-2 q^{12}+5 q^{11}-9 q^{10}+4 q^9+5 q^8-8 q^7+17 q^6-25 q^5+10 q^4+10 q^3-26 q^2+45 q-40+27 q^{-1} -84 q^{-3} +93 q^{-4} -24 q^{-5} +91 q^{-6} -33 q^{-7} -241 q^{-8} +117 q^{-9} +55 q^{-10} +279 q^{-11} -47 q^{-12} -536 q^{-13} +23 q^{-14} +151 q^{-15} +627 q^{-16} +59 q^{-17} -883 q^{-18} -231 q^{-19} +136 q^{-20} +1018 q^{-21} +324 q^{-22} -1092 q^{-23} -528 q^{-24} -57 q^{-25} +1253 q^{-26} +633 q^{-27} -1067 q^{-28} -694 q^{-29} -327 q^{-30} +1243 q^{-31} +830 q^{-32} -864 q^{-33} -676 q^{-34} -564 q^{-35} +1046 q^{-36} +893 q^{-37} -576 q^{-38} -546 q^{-39} -735 q^{-40} +745 q^{-41} +855 q^{-42} -246 q^{-43} -342 q^{-44} -835 q^{-45} +378 q^{-46} +716 q^{-47} +69 q^{-48} -74 q^{-49} -804 q^{-50} +19 q^{-51} +452 q^{-52} +254 q^{-53} +199 q^{-54} -597 q^{-55} -202 q^{-56} +136 q^{-57} +231 q^{-58} +346 q^{-59} -289 q^{-60} -210 q^{-61} -81 q^{-62} +79 q^{-63} +299 q^{-64} -56 q^{-65} -89 q^{-66} -115 q^{-67} -38 q^{-68} +148 q^{-69} +22 q^{-70} +4 q^{-71} -54 q^{-72} -49 q^{-73} +40 q^{-74} +11 q^{-75} +17 q^{-76} -8 q^{-77} -18 q^{-78} +5 q^{-79} +5 q^{-81} -3 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, 38]]</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, 38]]</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, 10, 4, 11], 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, 10, 4, 11], 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, 38]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_38_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, 38]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_38_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, 38]]&) /@ {~~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, 38]]&) /@ {
			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, 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>{Reversible, 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, 38]][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, 38]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:39, 30 August 2005

2005-08-30T14:39:14Z

Show changes

DrorsRobot at 01:06, 30 August 2005

2005-08-30T01:06:46Z

← Older revision		Revision as of 21:06, 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 22:16, 29 August 2005

2005-08-29T22:16:14Z

Show changes

ScottTestRobot at 00:12, 29 August 2005

2005-08-29T00:12:48Z

← Older revision		Revision as of 20:12, 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=38\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-3,6,-5,9,-10,2,-9,3,-7,8,-4,5,-6,4,-8,7/goTop.html}}
	{\| align=left
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=38\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-3,6,-5,9,-10,2,-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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	<tr align=center><td>-17</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>-17</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>-19</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>-19</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</nowiki></pre></td></tr>		q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:49, 28 August 2005

2005-08-28T01:49:26Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:49:51Z

Resetting knot page to basic template.

New page

10 38 - Revision history

ScottTestRobot at 22:03, 1 September 2005

DrorsRobot at 22:50, 31 August 2005

ScottKnotPageRobot at 14:39, 30 August 2005

DrorsRobot at 01:06, 30 August 2005

DrorsRobot at 22:16, 29 August 2005

ScottTestRobot at 00:12, 29 August 2005

ScottTestRobot at 01:49, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.