T(15,2) - Revision history

ScottKnotPageRobot at 15:37, 31 August 2005

2005-08-31T15:37:18Z

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-<!-- This page was  generated from the splice template "Torus_Knot_Splice_Template". Please do not edit! -->
+<!-- This page was generated from the splice template [[Torus_Knot_Splice_Base]]. Please do not edit!
 {{Torus Knot Page|
 m = 15 |

ScottKnotPageRobot at 16:15, 30 August 2005

2005-08-30T16:15:00Z

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ScottTestRobot at 00:44, 29 August 2005

2005-08-29T00:44:38Z

← Older revision		Revision as of 20:44, 28 August 2005
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	<!-- -->		<!-- -->
			<!-- This knot page was produced from [[Torus Knots Splice Template]] -->

	<!-- -->		<!-- -->
			<!-- -->

	<span id="top"></span>		<span id="top"></span>
			<!-- -->

	{{Knot Navigation Links\|ext=jpg}}		{{Knot Navigation Links\|ext=jpg}}

		⚫	{{Torus Knot Page Header\|m=15\|n=2\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-8,9,-10,11,-12,13,-14,15,-1,2,-3,4,-5,6,-7,8,-9,10,-11,12,-13,14,-15,1,-2,3,-4,5,-6,7/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.jpg]]
⚫	\|{{Torus Knot ~~Site~~ ~~Links~~\|m=15\|n=2\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-8,9,-10,11,-12,13,-14,15,-1,2,-3,4,-5,6,-7,8,-9,10,-11,12,-13,14,-15,1,-2,3,-4,5,-6,7/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>
	<tr align=center>		<tr align=center>
	<td width=10.%><table cellpadding=0 cellspacing=0>		<td width=10.%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>15</td><td bgcolor=yellow>1</td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </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>15</td><td bgcolor=yellow>1</td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </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>13</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> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>		<tr align=center><td>13</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> </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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	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[2, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[2, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[TorusKnot[15, 2]][t]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[TorusKnot[15, 2]][t]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -7 -6 -5 -4 -3 -2 1 2 3 4 5		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -7 -6 -5 -4
	-1 + t - t + t - t + ~~t - t + - + t - t + t - t + t -~~		-1 + Alternating - Alternating + Alternating - Alternating +
⚫	t

		⚫	-3 -2 1
	6 7
			Alternating - Alternating + ----------- + Alternating -
⚫	t + t</nowiki></pre></td></tr>
			Alternating

			2 3 4 5
			Alternating + Alternating - Alternating + Alternating -

			6 7
		⚫	Alternating + Alternating</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[TorusKnot[15, 2]][z]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[TorusKnot[15, 2]][z]</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> 2 4 6 8 10 12 14		<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> 2 4 6 8 10 12 14
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	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 140}</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 140}</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[TorusKnot[15, 2]][q, t]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[TorusKnot[15, 2]][q, t]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 13 15 17 2 21 3 21 4 25 5 25 6 29 7		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 13 15 2 17 3 21 4 21
	q + q + q ~~t +~~ q t + q ~~t +~~ q t + q ~~t +~~ q t +		q + q + Alternating q + Alternating q + Alternating q +

			5 25 6 25 7 29
			Alternating q + Alternating q + Alternating q +

			8 29 9 33 10 33
			Alternating q + Alternating q + Alternating q +

	29 8 33 9 33 10 37 11 37 12 41 13 41 14		11 37 12 37 13 41
	q ~~t +~~ q t + q ~~t +~~ q t + q ~~t +~~ q ~~t + q t~~ +		Alternating q + Alternating q + Alternating q +

			14 41 15 45
	45 15
	q t</nowiki></pre></td></tr>		Alternating q + Alternating q</nowiki></pre></td></tr>
	</table>		</table>

	{{Category:Knot Page}}		[[Category:Knot Page]]

ScottTestRobot at 23:42, 28 August 2005

2005-08-28T23:42:09Z

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 <!--  -->
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 |- valign=top
 |[[Image:{{PAGENAME}}.jpg]]
-|Visit [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-8,9,-10,11,-12,13,-14,15,-1,2,-3,4,-5,6,-7,8,-9,10,-11,12,-13,14,-15,1,-2,3,-4,5,-6,7/goTop.html {{PAGENAME}}'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]!
+|{{Torus Knot Site Links|m=15|n=2|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-8,9,-10,11,-12,13,-14,15,-1,2,-3,4,-5,6,-7,8,-9,10,-11,12,-13,14,-15,1,-2,3,-4,5,-6,7/goTop.html}}
 {{:{{PAGENAME}} Quick Notes}}
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 {{Knot Presentations}}
 {{Polynomial Invariants}}
 {{Vassiliev Invariants}}
@@ Line 182: / Line 166: @@
   q   t</nowiki></pre></td></tr>
 </table>

ScottTestRobot at 01:24, 28 August 2005

2005-08-28T01:24:30Z

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DrorsRobot at 02:46, 27 August 2005

2005-08-27T02:46:12Z

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DrorsRobot at 23:35, 26 August 2005

2005-08-26T23:35:34Z

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DrorsRobot at 23:33, 26 August 2005

2005-08-26T23:33:22Z

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 <!-- Script generated - do not edit! -->
-a $Failed></tr>
+-$Failed+ borde $Failed < $Fa
 q + q  + q  t  + q  t</nowiki></pre></td></tr>
-</table></math>
+</table>

DrorsRobot at 23:28, 26 August 2005

2005-08-26T23:28:45Z

New page

<!-- $Failedailedn.matuwo . ca
--------
c$Faidml K$FaidaFaedsKiledaidtt$edaidts$Faeds$Failedl$Failedail$Failedd$Fai$FailedFailed (Dowk-Thistlewaite) Codes|DowrhtFaileda$FaediaInvariants|name=T(3,2$Failed=$Failedinite $Failediev)nvaanFl=$iled''$Faileddding-left: 1em;"$Fail$Failed}$FailedhovHomo$Failedfi oven$Failed> are shoFaile</math>, over ternation < math</math>). e sques with <f$FailedYe2</math>, where <math>s=</th > 2 the signHLRed$Failedrder=1>
<tr cter>
<td wid$Failedled$Fai$Failed$Failed/tr>
</tab$Failed<td wi$F$$Failed;</td><td>&nbsp$Failedtd bgcolor=yellow>1</$Fl$Failed$Failed > $Failed > $Faailed style="color: red; borpding:0d;$Failed=$Failed $Failedn$Failedi$Failedn$Failedp $Failedd$Fae$Failepadding:0"><nowiki>PD[TorusKnot[3, 2]]</now$Failededp$Failed $Failedo$F$$Failedleds$Failedi$Failed<$Failedo$ilede$Failedk$Failedi$Failedp$Failde[-2, 3, -1, 2, -3, 1]</nowiki></pre></td></$Failedolor: bl$$Failed/$Failedrd$Failedo$Faed > $Failea$FailedFailedd$Failed ($Failedn0rpadding:0)Failed3$Failedr$Failed: $Failed  </now$Failed=borde $Failed - t
-($Failediled < $Fai
$Failed$Failedailedd$Failed>$Failede$Failed $Failede$Failed 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><t$Failedadding: 0$Faedlede$Failedm$Faid&$Failedr$Failed<$Faed > $Fail<$FailedK$Failedt$Failede$Failed $Failednowiki>Out[9]=   </nowiki></pre></td><td><$FailedFailedrpaddin $FailedFailed:$ilede$Failedt$Failedd$Failed>$Failedd$Failedt$Failedcpadding0$Failed"8ding: 0em"><nowiki>Select[AllK$Failed1/q) === Jo2[#1] ($Failedr$Failedp$Failed:$Fai)do$Failed>$Failedl$Failedn$Failedl$Failede$Failede$Failedr$Failedd$Failedl$Failed1$Failedi></pre></td><td><pre style="color: black; border: 0px; paddin$Failed2 14
q + q +$Failed<$Failedl$Failed:d$Failedr$Failed $Failed,$Failed>$Failedo$Failedl$Failed -8 z $Failed- 2
a $Failed></tr>
<tr valign=top><td><pre style="color: blue; $Failed]:=</nowiki></pre$Failedr$Failedn$Failed[$Failedi$Failed>$Failed>$FailedO$Failedp$Failed:$Failedc$Failed>$Failedr$Failedw$Failed<$Failed="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 5 2 9 3
q + q + q t + q t</nowiki></pre></td></tr>
</table></math>