ScottTestRobot at 22:01, 1 September 2005

2005-09-01T22:01:53Z

DrorsRobot at 22:47, 31 August 2005

2005-08-31T22:47:21Z

← Older revision		Revision as of 18:47, 31 August 2005
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	coloured_jones_3 = <math>-2 q^{35}+4 q^{34}+3 q^{33}-24 q^{31}+47 q^{29}+25 q^{28}-80 q^{27}-77 q^{26}+114 q^{25}+147 q^{24}-124 q^{23}-238 q^{22}+115 q^{21}+324 q^{20}-79 q^{19}-402 q^{18}+38 q^{17}+445 q^{16}+20 q^{15}-473 q^{14}-67 q^{13}+468 q^{12}+117 q^{11}-448 q^{10}-158 q^9+404 q^8+198 q^7-344 q^6-227 q^5+266 q^4+247 q^3-185 q^2-236 q+94+212 q^{-1} -26 q^{-2} -160 q^{-3} -23 q^{-4} +106 q^{-5} +38 q^{-6} -51 q^{-7} -40 q^{-8} +23 q^{-9} +21 q^{-10} -4 q^{-11} -9 q^{-12} - q^{-13} +4 q^{-14} - q^{-15} </math> \|		coloured_jones_3 = <math>-2 q^{35}+4 q^{34}+3 q^{33}-24 q^{31}+47 q^{29}+25 q^{28}-80 q^{27}-77 q^{26}+114 q^{25}+147 q^{24}-124 q^{23}-238 q^{22}+115 q^{21}+324 q^{20}-79 q^{19}-402 q^{18}+38 q^{17}+445 q^{16}+20 q^{15}-473 q^{14}-67 q^{13}+468 q^{12}+117 q^{11}-448 q^{10}-158 q^9+404 q^8+198 q^7-344 q^6-227 q^5+266 q^4+247 q^3-185 q^2-236 q+94+212 q^{-1} -26 q^{-2} -160 q^{-3} -23 q^{-4} +106 q^{-5} +38 q^{-6} -51 q^{-7} -40 q^{-8} +23 q^{-9} +21 q^{-10} -4 q^{-11} -9 q^{-12} - q^{-13} +4 q^{-14} - q^{-15} </math> \|
	coloured_jones_4 = <math>q^{58}-6 q^{56}-5 q^{55}+14 q^{54}+20 q^{53}+13 q^{52}-45 q^{51}-95 q^{50}+17 q^{49}+131 q^{48}+199 q^{47}-42 q^{46}-420 q^{45}-244 q^{44}+193 q^{43}+746 q^{42}+386 q^{41}-778 q^{40}-975 q^{39}-252 q^{38}+1364 q^{37}+1404 q^{36}-650 q^{35}-1793 q^{34}-1302 q^{33}+1511 q^{32}+2518 q^{31}+29 q^{30}-2147 q^{29}-2414 q^{28}+1131 q^{27}+3155 q^{26}+806 q^{25}-1975 q^{24}-3103 q^{23}+574 q^{22}+3243 q^{21}+1350 q^{20}-1534 q^{19}-3322 q^{18}+35 q^{17}+2942 q^{16}+1691 q^{15}-925 q^{14}-3196 q^{13}-538 q^{12}+2306 q^{11}+1887 q^{10}-126 q^9-2693 q^8-1091 q^7+1316 q^6+1764 q^5+703 q^4-1745 q^3-1298 q^2+225 q+1149+1109 q^{-1} -634 q^{-2} -923 q^{-3} -423 q^{-4} +330 q^{-5} +851 q^{-6} +55 q^{-7} -296 q^{-8} -400 q^{-9} -128 q^{-10} +328 q^{-11} +148 q^{-12} +38 q^{-13} -131 q^{-14} -130 q^{-15} +49 q^{-16} +36 q^{-17} +47 q^{-18} -8 q^{-19} -33 q^{-20} + q^{-21} - q^{-22} +9 q^{-23} + q^{-24} -4 q^{-25} + q^{-26} </math> \|		coloured_jones_4 = <math>q^{58}-6 q^{56}-5 q^{55}+14 q^{54}+20 q^{53}+13 q^{52}-45 q^{51}-95 q^{50}+17 q^{49}+131 q^{48}+199 q^{47}-42 q^{46}-420 q^{45}-244 q^{44}+193 q^{43}+746 q^{42}+386 q^{41}-778 q^{40}-975 q^{39}-252 q^{38}+1364 q^{37}+1404 q^{36}-650 q^{35}-1793 q^{34}-1302 q^{33}+1511 q^{32}+2518 q^{31}+29 q^{30}-2147 q^{29}-2414 q^{28}+1131 q^{27}+3155 q^{26}+806 q^{25}-1975 q^{24}-3103 q^{23}+574 q^{22}+3243 q^{21}+1350 q^{20}-1534 q^{19}-3322 q^{18}+35 q^{17}+2942 q^{16}+1691 q^{15}-925 q^{14}-3196 q^{13}-538 q^{12}+2306 q^{11}+1887 q^{10}-126 q^9-2693 q^8-1091 q^7+1316 q^6+1764 q^5+703 q^4-1745 q^3-1298 q^2+225 q+1149+1109 q^{-1} -634 q^{-2} -923 q^{-3} -423 q^{-4} +330 q^{-5} +851 q^{-6} +55 q^{-7} -296 q^{-8} -400 q^{-9} -128 q^{-10} +328 q^{-11} +148 q^{-12} +38 q^{-13} -131 q^{-14} -130 q^{-15} +49 q^{-16} +36 q^{-17} +47 q^{-18} -8 q^{-19} -33 q^{-20} + q^{-21} - q^{-22} +9 q^{-23} + q^{-24} -4 q^{-25} + q^{-26} </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, 163]]</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, 163]]</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[8, 3, 9, 4], X[13, 19, 14, 18], X[11, 1, 12, 20],		<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[8, 3, 9, 4], X[13, 19, 14, 18], X[11, 1, 12, 20],
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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>4</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>4</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, 163]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_163_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, 163]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_163_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, 163]]&) /@ {~~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, 163]]&) /@ {
			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}, 3, 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, {1, 2}, 3, 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, 163]][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, 163]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:37, 30 August 2005

2005-08-30T14:37:48Z

Show changes

DrorsRobot at 01:05, 30 August 2005

2005-08-30T01:05:12Z

← Older revision		Revision as of 21:05, 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 22:27, 29 August 2005

2005-08-29T22:27:55Z

Show changes

ScottTestRobot at 00:11, 29 August 2005

2005-08-29T00:11:08Z

← Older revision		Revision as of 20:11, 28 August 2005
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			<!-- -->
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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=163\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-6,2,-7,8,-1,9,-2,10,-8,-4,5,-3,-9,6,-10,7,3,-5,4/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=163\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-6,2,-7,8,-1,9,-2,10,-8,-4,5,-3,-9,6,-10,7,3,-5,4/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>
	<tr align=center>		<tr align=center>
	<td width=15.3846%><table cellpadding=0 cellspacing=0>		<td width=15.3846%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>3</td></tr>		<tr align=center><td>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>3</td></tr>
	<tr align=center><td>-5</td><td bgcolor=yellow>1</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>-5</td><td bgcolor=yellow>1</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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	4 q t + 5 q t + 3 q t + 4 q t + 2 q t + 3 q t + 2 q t</nowiki></pre></td></tr>		4 q t + 5 q t + 3 q t + 4 q t + 2 q t + 3 q t + 2 q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:47, 28 August 2005

2005-08-28T01:47:50Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:48Z

Resetting knot page to basic template.

New page

10 163 - Revision history

ScottTestRobot at 22:01, 1 September 2005

DrorsRobot at 22:47, 31 August 2005

ScottKnotPageRobot at 14:37, 30 August 2005

DrorsRobot at 01:05, 30 August 2005

DrorsRobot at 22:27, 29 August 2005

ScottTestRobot at 00:11, 29 August 2005

ScottTestRobot at 01:47, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.