ScottTestRobot at 22:06, 1 September 2005

2005-09-01T22:06:14Z

DrorsRobot at 22:39, 31 August 2005

2005-08-31T22:39:52Z

← Older revision		Revision as of 18:39, 31 August 2005
Line 1:		Line 1:
			<!-- WARNING! WARNING! WARNING!
	<!-- This page was generated from the splice template ~~"Rolfsen_Splice_Template"~~. Please do not edit! ~~-->~~		<!-- This page was generated from the splice template [[Rolfsen_Splice_Base]]. Please do not edit!
	<!-- --> <!--
			<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)
	-->
			<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Rolfsen_Splice_Base]]. -->
			<!-- <math>\text{Null}</math> -->
			<!-- <math>\text{Null}</math> -->
	{{Rolfsen Knot Page\|		{{Rolfsen Knot Page\|
	n = 10 \|		n = 10 \|
Line 41:		Line 44:
	coloured_jones_3 = <math>q^{54}-3 q^{53}+2 q^{52}+2 q^{51}-q^{50}-7 q^{49}+6 q^{48}+14 q^{47}-15 q^{46}-28 q^{45}+29 q^{44}+53 q^{43}-42 q^{42}-99 q^{41}+55 q^{40}+159 q^{39}-59 q^{38}-227 q^{37}+44 q^{36}+305 q^{35}-23 q^{34}-365 q^{33}-20 q^{32}+419 q^{31}+57 q^{30}-438 q^{29}-108 q^{28}+445 q^{27}+148 q^{26}-422 q^{25}-190 q^{24}+385 q^{23}+222 q^{22}-331 q^{21}-242 q^{20}+258 q^{19}+260 q^{18}-195 q^{17}-244 q^{16}+113 q^{15}+230 q^{14}-59 q^{13}-183 q^{12}+3 q^{11}+146 q^{10}+16 q^9-91 q^8-35 q^7+62 q^6+25 q^5-28 q^4-23 q^3+17 q^2+11 q-5-8 q^{-1} +4 q^{-2} +2 q^{-3} -2 q^{-5} + q^{-6} </math> \|		coloured_jones_3 = <math>q^{54}-3 q^{53}+2 q^{52}+2 q^{51}-q^{50}-7 q^{49}+6 q^{48}+14 q^{47}-15 q^{46}-28 q^{45}+29 q^{44}+53 q^{43}-42 q^{42}-99 q^{41}+55 q^{40}+159 q^{39}-59 q^{38}-227 q^{37}+44 q^{36}+305 q^{35}-23 q^{34}-365 q^{33}-20 q^{32}+419 q^{31}+57 q^{30}-438 q^{29}-108 q^{28}+445 q^{27}+148 q^{26}-422 q^{25}-190 q^{24}+385 q^{23}+222 q^{22}-331 q^{21}-242 q^{20}+258 q^{19}+260 q^{18}-195 q^{17}-244 q^{16}+113 q^{15}+230 q^{14}-59 q^{13}-183 q^{12}+3 q^{11}+146 q^{10}+16 q^9-91 q^8-35 q^7+62 q^6+25 q^5-28 q^4-23 q^3+17 q^2+11 q-5-8 q^{-1} +4 q^{-2} +2 q^{-3} -2 q^{-5} + q^{-6} </math> \|
	coloured_jones_4 = <math>q^{88}-3 q^{87}+2 q^{86}+2 q^{85}-5 q^{84}+8 q^{83}-10 q^{82}+8 q^{81}+4 q^{80}-26 q^{79}+28 q^{78}-19 q^{77}+36 q^{76}+12 q^{75}-104 q^{74}+33 q^{73}-17 q^{72}+160 q^{71}+78 q^{70}-287 q^{69}-90 q^{68}-83 q^{67}+462 q^{66}+377 q^{65}-494 q^{64}-461 q^{63}-416 q^{62}+852 q^{61}+1018 q^{60}-485 q^{59}-954 q^{58}-1114 q^{57}+1046 q^{56}+1813 q^{55}-132 q^{54}-1264 q^{53}-1944 q^{52}+897 q^{51}+2385 q^{50}+393 q^{49}-1216 q^{48}-2554 q^{47}+520 q^{46}+2537 q^{45}+841 q^{44}-888 q^{43}-2784 q^{42}+83 q^{41}+2309 q^{40}+1132 q^{39}-404 q^{38}-2678 q^{37}-358 q^{36}+1807 q^{35}+1276 q^{34}+163 q^{33}-2275 q^{32}-756 q^{31}+1089 q^{30}+1224 q^{29}+713 q^{28}-1600 q^{27}-956 q^{26}+312 q^{25}+892 q^{24}+1019 q^{23}-796 q^{22}-805 q^{21}-244 q^{20}+375 q^{19}+921 q^{18}-170 q^{17}-410 q^{16}-386 q^{15}-31 q^{14}+550 q^{13}+81 q^{12}-74 q^{11}-241 q^{10}-153 q^9+216 q^8+69 q^7+45 q^6-80 q^5-100 q^4+60 q^3+15 q^2+35 q-14-37 q^{-1} +17 q^{-2} -2 q^{-3} +11 q^{-4} - q^{-5} -10 q^{-6} +5 q^{-7} - q^{-8} +2 q^{-9} -2 q^{-11} + q^{-12} </math> \|		coloured_jones_4 = <math>q^{88}-3 q^{87}+2 q^{86}+2 q^{85}-5 q^{84}+8 q^{83}-10 q^{82}+8 q^{81}+4 q^{80}-26 q^{79}+28 q^{78}-19 q^{77}+36 q^{76}+12 q^{75}-104 q^{74}+33 q^{73}-17 q^{72}+160 q^{71}+78 q^{70}-287 q^{69}-90 q^{68}-83 q^{67}+462 q^{66}+377 q^{65}-494 q^{64}-461 q^{63}-416 q^{62}+852 q^{61}+1018 q^{60}-485 q^{59}-954 q^{58}-1114 q^{57}+1046 q^{56}+1813 q^{55}-132 q^{54}-1264 q^{53}-1944 q^{52}+897 q^{51}+2385 q^{50}+393 q^{49}-1216 q^{48}-2554 q^{47}+520 q^{46}+2537 q^{45}+841 q^{44}-888 q^{43}-2784 q^{42}+83 q^{41}+2309 q^{40}+1132 q^{39}-404 q^{38}-2678 q^{37}-358 q^{36}+1807 q^{35}+1276 q^{34}+163 q^{33}-2275 q^{32}-756 q^{31}+1089 q^{30}+1224 q^{29}+713 q^{28}-1600 q^{27}-956 q^{26}+312 q^{25}+892 q^{24}+1019 q^{23}-796 q^{22}-805 q^{21}-244 q^{20}+375 q^{19}+921 q^{18}-170 q^{17}-410 q^{16}-386 q^{15}-31 q^{14}+550 q^{13}+81 q^{12}-74 q^{11}-241 q^{10}-153 q^9+216 q^8+69 q^7+45 q^6-80 q^5-100 q^4+60 q^3+15 q^2+35 q-14-37 q^{-1} +17 q^{-2} -2 q^{-3} +11 q^{-4} - q^{-5} -10 q^{-6} +5 q^{-7} - q^{-8} +2 q^{-9} -2 q^{-11} + q^{-12} </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>
Line 50:		Line 53:
	<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, 56]]</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, 56]]</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[4, 2, 5, 1], X[10, 4, 11, 3], X[12, 6, 13, 5], X[18, 14, 19, 13],		<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[4, 2, 5, 1], X[10, 4, 11, 3], X[12, 6, 13, 5], X[18, 14, 19, 13],
Line 70:		Line 73:
	<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, 56]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_56_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, 56]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_56_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, 56]]&) /@ {~~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, 56]]&) /@ {
			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, 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, 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, 56]][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, 56]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:32, 30 August 2005

2005-08-30T14:32:42Z

Show changes

DrorsRobot at 00:59, 30 August 2005

2005-08-30T00:59:27Z

← Older revision		Revision as of 20:59, 29 August 2005
Line 1:		Line 1:
			<!-- This page was generated from the splice template "Rolfsen_Splice_Template". Please do not edit! -->
	<!-- -->		<!-- -->
	<!-- -->		<!-- -->
Line 220:		Line 221:
	</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 21:57, 29 August 2005

2005-08-29T21:57:05Z

Show changes

ScottTestRobot at 00:05, 29 August 2005

2005-08-29T00:05:08Z

← Older revision		Revision as of 20:05, 28 August 2005
Line 1:		Line 1:
	<!-- -->		<!-- -->
			<!-- -->

			<!-- -->
			<!-- -->
	<!-- provide an anchor so we can return to the top of the page -->		<!-- provide an anchor so we can return to the top of the page -->
	<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=56\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,3,-6,5,-9,10,-2,9,-3,4,-8,7,-5,6,-4,8,-7/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=56\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,3,-6,5,-9,10,-2,9,-3,4,-8,7,-5,6,-4,8,-7/goTop.html}}
	\|{{:{{PAGENAME}} Quick Notes}}
	\|}

	<br style="clear:both" />		<br style="clear:both" />
Line 24:		Line 21:
	{{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=13.3333%><table cellpadding=0 cellspacing=0>		<td width=13.3333%><table cellpadding=0 cellspacing=0>
Line 48:		Line 41:
	<tr align=center><td>1</td><td bgcolor=yellow> </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>-1</td></tr>		<tr align=center><td>1</td><td bgcolor=yellow> </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>-1</td></tr>
	<tr align=center><td>-1</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>-1</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}}

Line 141:		Line 133:
	2 q t + 4 q t + q t + 2 q t + q t</nowiki></pre></td></tr>		2 q t + 4 q t + q t + 2 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:44, 28 August 2005

2005-08-28T01:44:09Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:08Z

Resetting knot page to basic template.

New page

10 56 - Revision history

ScottTestRobot at 22:06, 1 September 2005

DrorsRobot at 22:39, 31 August 2005

ScottKnotPageRobot at 14:32, 30 August 2005

DrorsRobot at 00:59, 30 August 2005

DrorsRobot at 21:57, 29 August 2005

ScottTestRobot at 00:05, 29 August 2005

ScottTestRobot at 01:44, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.