ScottTestRobot at 22:00, 1 September 2005

2005-09-01T22:00:50Z

DrorsRobot at 22:45, 31 August 2005

2005-08-31T22:45:40Z

← Older revision		Revision as of 18:45, 31 August 2005
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	coloured_jones_3 = <math>-q^{30}+3 q^{29}-q^{28}-4 q^{27}-q^{26}+11 q^{25}+2 q^{24}-21 q^{23}-6 q^{22}+35 q^{21}+15 q^{20}-54 q^{19}-31 q^{18}+74 q^{17}+62 q^{16}-99 q^{15}-98 q^{14}+110 q^{13}+156 q^{12}-123 q^{11}-209 q^{10}+113 q^9+275 q^8-103 q^7-327 q^6+77 q^5+373 q^4-50 q^3-399 q^2+15 q+413+15 q^{-1} -399 q^{-2} -50 q^{-3} +373 q^{-4} +77 q^{-5} -327 q^{-6} -103 q^{-7} +275 q^{-8} +113 q^{-9} -209 q^{-10} -123 q^{-11} +156 q^{-12} +110 q^{-13} -98 q^{-14} -99 q^{-15} +62 q^{-16} +74 q^{-17} -31 q^{-18} -54 q^{-19} +15 q^{-20} +35 q^{-21} -6 q^{-22} -21 q^{-23} +2 q^{-24} +11 q^{-25} - q^{-26} -4 q^{-27} - q^{-28} +3 q^{-29} - q^{-30} </math> \|		coloured_jones_3 = <math>-q^{30}+3 q^{29}-q^{28}-4 q^{27}-q^{26}+11 q^{25}+2 q^{24}-21 q^{23}-6 q^{22}+35 q^{21}+15 q^{20}-54 q^{19}-31 q^{18}+74 q^{17}+62 q^{16}-99 q^{15}-98 q^{14}+110 q^{13}+156 q^{12}-123 q^{11}-209 q^{10}+113 q^9+275 q^8-103 q^7-327 q^6+77 q^5+373 q^4-50 q^3-399 q^2+15 q+413+15 q^{-1} -399 q^{-2} -50 q^{-3} +373 q^{-4} +77 q^{-5} -327 q^{-6} -103 q^{-7} +275 q^{-8} +113 q^{-9} -209 q^{-10} -123 q^{-11} +156 q^{-12} +110 q^{-13} -98 q^{-14} -99 q^{-15} +62 q^{-16} +74 q^{-17} -31 q^{-18} -54 q^{-19} +15 q^{-20} +35 q^{-21} -6 q^{-22} -21 q^{-23} +2 q^{-24} +11 q^{-25} - q^{-26} -4 q^{-27} - q^{-28} +3 q^{-29} - q^{-30} </math> \|
	coloured_jones_4 = <math>q^{50}-3 q^{49}+q^{48}+4 q^{47}-3 q^{46}+4 q^{45}-14 q^{44}+6 q^{43}+18 q^{42}-13 q^{41}+12 q^{40}-47 q^{39}+15 q^{38}+61 q^{37}-25 q^{36}+20 q^{35}-129 q^{34}+19 q^{33}+153 q^{32}-2 q^{31}+50 q^{30}-302 q^{29}-50 q^{28}+273 q^{27}+127 q^{26}+197 q^{25}-548 q^{24}-286 q^{23}+292 q^{22}+351 q^{21}+584 q^{20}-725 q^{19}-681 q^{18}+73 q^{17}+529 q^{16}+1179 q^{15}-689 q^{14}-1071 q^{13}-356 q^{12}+531 q^{11}+1785 q^{10}-459 q^9-1299 q^8-814 q^7+369 q^6+2200 q^5-159 q^4-1320 q^3-1155 q^2+124 q+2345+124 q^{-1} -1155 q^{-2} -1320 q^{-3} -159 q^{-4} +2200 q^{-5} +369 q^{-6} -814 q^{-7} -1299 q^{-8} -459 q^{-9} +1785 q^{-10} +531 q^{-11} -356 q^{-12} -1071 q^{-13} -689 q^{-14} +1179 q^{-15} +529 q^{-16} +73 q^{-17} -681 q^{-18} -725 q^{-19} +584 q^{-20} +351 q^{-21} +292 q^{-22} -286 q^{-23} -548 q^{-24} +197 q^{-25} +127 q^{-26} +273 q^{-27} -50 q^{-28} -302 q^{-29} +50 q^{-30} -2 q^{-31} +153 q^{-32} +19 q^{-33} -129 q^{-34} +20 q^{-35} -25 q^{-36} +61 q^{-37} +15 q^{-38} -47 q^{-39} +12 q^{-40} -13 q^{-41} +18 q^{-42} +6 q^{-43} -14 q^{-44} +4 q^{-45} -3 q^{-46} +4 q^{-47} + q^{-48} -3 q^{-49} + q^{-50} </math> \|		coloured_jones_4 = <math>q^{50}-3 q^{49}+q^{48}+4 q^{47}-3 q^{46}+4 q^{45}-14 q^{44}+6 q^{43}+18 q^{42}-13 q^{41}+12 q^{40}-47 q^{39}+15 q^{38}+61 q^{37}-25 q^{36}+20 q^{35}-129 q^{34}+19 q^{33}+153 q^{32}-2 q^{31}+50 q^{30}-302 q^{29}-50 q^{28}+273 q^{27}+127 q^{26}+197 q^{25}-548 q^{24}-286 q^{23}+292 q^{22}+351 q^{21}+584 q^{20}-725 q^{19}-681 q^{18}+73 q^{17}+529 q^{16}+1179 q^{15}-689 q^{14}-1071 q^{13}-356 q^{12}+531 q^{11}+1785 q^{10}-459 q^9-1299 q^8-814 q^7+369 q^6+2200 q^5-159 q^4-1320 q^3-1155 q^2+124 q+2345+124 q^{-1} -1155 q^{-2} -1320 q^{-3} -159 q^{-4} +2200 q^{-5} +369 q^{-6} -814 q^{-7} -1299 q^{-8} -459 q^{-9} +1785 q^{-10} +531 q^{-11} -356 q^{-12} -1071 q^{-13} -689 q^{-14} +1179 q^{-15} +529 q^{-16} +73 q^{-17} -681 q^{-18} -725 q^{-19} +584 q^{-20} +351 q^{-21} +292 q^{-22} -286 q^{-23} -548 q^{-24} +197 q^{-25} +127 q^{-26} +273 q^{-27} -50 q^{-28} -302 q^{-29} +50 q^{-30} -2 q^{-31} +153 q^{-32} +19 q^{-33} -129 q^{-34} +20 q^{-35} -25 q^{-36} +61 q^{-37} +15 q^{-38} -47 q^{-39} +12 q^{-40} -13 q^{-41} +18 q^{-42} +6 q^{-43} -14 q^{-44} +4 q^{-45} -3 q^{-46} +4 q^{-47} + q^{-48} -3 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, 33]]</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, 33]]</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[6, 2, 7, 1], X[14, 6, 15, 5], X[20, 15, 1, 16], X[16, 7, 17, 8],		<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[6, 2, 7, 1], X[14, 6, 15, 5], X[20, 15, 1, 16], X[16, 7, 17, 8],
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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, 33]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_33_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, 33]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_33_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, 33]]&) /@ {~~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, 33]]&) /@ {
			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, 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>{FullyAmphicheiral, 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, 33]][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, 33]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:36, 30 August 2005

2005-08-30T14:36:41Z

Show changes

DrorsRobot at 01:04, 30 August 2005

2005-08-30T01:04:00Z

← 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 22:16, 29 August 2005

2005-08-29T22:16:04Z

Show changes

ScottTestRobot at 00:09, 29 August 2005

2005-08-29T00:09:52Z

← Older revision		Revision as of 20:09, 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=33\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-8,9,-10,2,-1,4,-5,6,-7,10,-9,8,-2,3,-4,7,-6,5,-3/goTop.html}}
	{\| align=left
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=33\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-8,9,-10,2,-1,4,-5,6,-7,10,-9,8,-2,3,-4,7,-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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	<tr align=center><td>-9</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>-9</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>-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 + 2 q t + q t</nowiki></pre></td></tr>		q t + 2 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:46, 28 August 2005

2005-08-28T01:46:57Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:49:47Z

Resetting knot page to basic template.

New page

10 33 - Revision history

ScottTestRobot at 22:00, 1 September 2005

DrorsRobot at 22:45, 31 August 2005

ScottKnotPageRobot at 14:36, 30 August 2005

DrorsRobot at 01:04, 30 August 2005

DrorsRobot at 22:16, 29 August 2005

ScottTestRobot at 00:09, 29 August 2005

ScottTestRobot at 01:46, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.