ScottTestRobot at 22:01, 1 September 2005

2005-09-01T22:01:08Z

DrorsRobot at 22:46, 31 August 2005

2005-08-31T22:46:07Z

← Older revision		Revision as of 18:46, 31 August 2005
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	{{Rolfsen Knot Page\|		{{Rolfsen Knot Page\|
	n = 10 \|		n = 10 \|
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	coloured_jones_3 = <math>-q^{42}+2 q^{41}+q^{40}-2 q^{39}-5 q^{38}+4 q^{37}+9 q^{36}-3 q^{35}-17 q^{34}+q^{33}+23 q^{32}+7 q^{31}-30 q^{30}-15 q^{29}+33 q^{28}+25 q^{27}-31 q^{26}-36 q^{25}+28 q^{24}+40 q^{23}-19 q^{22}-45 q^{21}+13 q^{20}+42 q^{19}-3 q^{18}-41 q^{17}+32 q^{15}+9 q^{14}-27 q^{13}-11 q^{12}+15 q^{11}+17 q^{10}-8 q^9-17 q^8-2 q^7+17 q^6+8 q^5-12 q^4-13 q^3+9 q^2+8 q+2-7 q^{-1} -3 q^{-2} -3 q^{-3} +11 q^{-4} +4 q^{-5} -6 q^{-6} -13 q^{-7} +10 q^{-8} +9 q^{-9} -4 q^{-10} -11 q^{-11} +4 q^{-12} +7 q^{-13} -2 q^{-14} -3 q^{-15} - q^{-16} +3 q^{-17} - q^{-18} </math> \|		coloured_jones_3 = <math>-q^{42}+2 q^{41}+q^{40}-2 q^{39}-5 q^{38}+4 q^{37}+9 q^{36}-3 q^{35}-17 q^{34}+q^{33}+23 q^{32}+7 q^{31}-30 q^{30}-15 q^{29}+33 q^{28}+25 q^{27}-31 q^{26}-36 q^{25}+28 q^{24}+40 q^{23}-19 q^{22}-45 q^{21}+13 q^{20}+42 q^{19}-3 q^{18}-41 q^{17}+32 q^{15}+9 q^{14}-27 q^{13}-11 q^{12}+15 q^{11}+17 q^{10}-8 q^9-17 q^8-2 q^7+17 q^6+8 q^5-12 q^4-13 q^3+9 q^2+8 q+2-7 q^{-1} -3 q^{-2} -3 q^{-3} +11 q^{-4} +4 q^{-5} -6 q^{-6} -13 q^{-7} +10 q^{-8} +9 q^{-9} -4 q^{-10} -11 q^{-11} +4 q^{-12} +7 q^{-13} -2 q^{-14} -3 q^{-15} - q^{-16} +3 q^{-17} - q^{-18} </math> \|
	coloured_jones_4 = <math>q^{70}-2 q^{69}-q^{68}+2 q^{67}+q^{66}+6 q^{65}-8 q^{64}-7 q^{63}+2 q^{62}+3 q^{61}+26 q^{60}-12 q^{59}-23 q^{58}-11 q^{57}-5 q^{56}+63 q^{55}+3 q^{54}-30 q^{53}-37 q^{52}-44 q^{51}+93 q^{50}+33 q^{49}-7 q^{48}-47 q^{47}-101 q^{46}+92 q^{45}+41 q^{44}+30 q^{43}-20 q^{42}-135 q^{41}+80 q^{40}+10 q^{39}+38 q^{38}+20 q^{37}-126 q^{36}+97 q^{35}-33 q^{34}+31 q^{32}-96 q^{31}+156 q^{30}-53 q^{29}-65 q^{28}+3 q^{27}-71 q^{26}+234 q^{25}-45 q^{24}-127 q^{23}-44 q^{22}-58 q^{21}+309 q^{20}-24 q^{19}-183 q^{18}-95 q^{17}-45 q^{16}+374 q^{15}+4 q^{14}-227 q^{13}-148 q^{12}-44 q^{11}+416 q^{10}+50 q^9-236 q^8-195 q^7-72 q^6+404 q^5+101 q^4-183 q^3-201 q^2-119 q+324+122 q^{-1} -95 q^{-2} -153 q^{-3} -141 q^{-4} +208 q^{-5} +96 q^{-6} -22 q^{-7} -80 q^{-8} -125 q^{-9} +110 q^{-10} +52 q^{-11} +11 q^{-12} -25 q^{-13} -85 q^{-14} +49 q^{-15} +17 q^{-16} +16 q^{-17} - q^{-18} -44 q^{-19} +19 q^{-20} +2 q^{-21} +9 q^{-22} +3 q^{-23} -15 q^{-24} +5 q^{-25} - q^{-26} +3 q^{-27} + q^{-28} -3 q^{-29} + q^{-30} </math> \|		coloured_jones_4 = <math>q^{70}-2 q^{69}-q^{68}+2 q^{67}+q^{66}+6 q^{65}-8 q^{64}-7 q^{63}+2 q^{62}+3 q^{61}+26 q^{60}-12 q^{59}-23 q^{58}-11 q^{57}-5 q^{56}+63 q^{55}+3 q^{54}-30 q^{53}-37 q^{52}-44 q^{51}+93 q^{50}+33 q^{49}-7 q^{48}-47 q^{47}-101 q^{46}+92 q^{45}+41 q^{44}+30 q^{43}-20 q^{42}-135 q^{41}+80 q^{40}+10 q^{39}+38 q^{38}+20 q^{37}-126 q^{36}+97 q^{35}-33 q^{34}+31 q^{32}-96 q^{31}+156 q^{30}-53 q^{29}-65 q^{28}+3 q^{27}-71 q^{26}+234 q^{25}-45 q^{24}-127 q^{23}-44 q^{22}-58 q^{21}+309 q^{20}-24 q^{19}-183 q^{18}-95 q^{17}-45 q^{16}+374 q^{15}+4 q^{14}-227 q^{13}-148 q^{12}-44 q^{11}+416 q^{10}+50 q^9-236 q^8-195 q^7-72 q^6+404 q^5+101 q^4-183 q^3-201 q^2-119 q+324+122 q^{-1} -95 q^{-2} -153 q^{-3} -141 q^{-4} +208 q^{-5} +96 q^{-6} -22 q^{-7} -80 q^{-8} -125 q^{-9} +110 q^{-10} +52 q^{-11} +11 q^{-12} -25 q^{-13} -85 q^{-14} +49 q^{-15} +17 q^{-16} +16 q^{-17} - q^{-18} -44 q^{-19} +19 q^{-20} +2 q^{-21} +9 q^{-22} +3 q^{-23} -15 q^{-24} +5 q^{-25} - q^{-26} +3 q^{-27} + q^{-28} -3 q^{-29} + q^{-30} </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, 10]]</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, 10]]</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, 12, 4, 13], X[13, 1, 14, 20], X[5, 15, 6, 14],		<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, 12, 4, 13], X[13, 1, 14, 20], X[5, 15, 6, 14],
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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, 10]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_10_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, 10]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_10_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, 10]]&) /@ {~~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, 10]]&) /@ {
			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, 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, 1, 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, 10]][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, 10]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:37, 30 August 2005

2005-08-30T14:37:04Z

Show changes

DrorsRobot at 01:04, 30 August 2005

2005-08-30T01:04:20Z

← Older revision		Revision as of 21:04, 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 22:14, 29 August 2005

2005-08-29T22:14:03Z

Show changes

ScottTestRobot at 00:10, 29 August 2005

2005-08-29T00:10:11Z

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

			[[Category:Knot Page]]

ScottTestRobot at 01:47, 28 August 2005

2005-08-28T01:47:10Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:49:27Z

Resetting knot page to basic template.

New page

10 10 - Revision history

ScottTestRobot at 22:01, 1 September 2005

DrorsRobot at 22:46, 31 August 2005

ScottKnotPageRobot at 14:37, 30 August 2005

DrorsRobot at 01:04, 30 August 2005

DrorsRobot at 22:14, 29 August 2005

ScottTestRobot at 00:10, 29 August 2005

ScottTestRobot at 01:47, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.