ScottTestRobot at 22:04, 1 September 2005

2005-09-01T22:04:45Z

DrorsRobot at 22:53, 31 August 2005

2005-08-31T22:53:01Z

← Older revision		Revision as of 18:53, 31 August 2005
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	coloured_jones_3 = <math>q^{54}-3 q^{53}+2 q^{52}+3 q^{51}-q^{50}-10 q^{49}+3 q^{48}+21 q^{47}-5 q^{46}-39 q^{45}+6 q^{44}+64 q^{43}+3 q^{42}-107 q^{41}-13 q^{40}+150 q^{39}+40 q^{38}-199 q^{37}-73 q^{36}+241 q^{35}+114 q^{34}-272 q^{33}-157 q^{32}+292 q^{31}+189 q^{30}-286 q^{29}-226 q^{28}+277 q^{27}+239 q^{26}-240 q^{25}-259 q^{24}+210 q^{23}+252 q^{22}-156 q^{21}-248 q^{20}+109 q^{19}+228 q^{18}-64 q^{17}-194 q^{16}+18 q^{15}+162 q^{14}+5 q^{13}-112 q^{12}-30 q^{11}+83 q^{10}+23 q^9-39 q^8-31 q^7+29 q^6+12 q^5-7 q^4-13 q^3+8 q^2+2 q-4 q^{-1} +3 q^{-2} - q^{-5} + q^{-6} </math> \|		coloured_jones_3 = <math>q^{54}-3 q^{53}+2 q^{52}+3 q^{51}-q^{50}-10 q^{49}+3 q^{48}+21 q^{47}-5 q^{46}-39 q^{45}+6 q^{44}+64 q^{43}+3 q^{42}-107 q^{41}-13 q^{40}+150 q^{39}+40 q^{38}-199 q^{37}-73 q^{36}+241 q^{35}+114 q^{34}-272 q^{33}-157 q^{32}+292 q^{31}+189 q^{30}-286 q^{29}-226 q^{28}+277 q^{27}+239 q^{26}-240 q^{25}-259 q^{24}+210 q^{23}+252 q^{22}-156 q^{21}-248 q^{20}+109 q^{19}+228 q^{18}-64 q^{17}-194 q^{16}+18 q^{15}+162 q^{14}+5 q^{13}-112 q^{12}-30 q^{11}+83 q^{10}+23 q^9-39 q^8-31 q^7+29 q^6+12 q^5-7 q^4-13 q^3+8 q^2+2 q-4 q^{-1} +3 q^{-2} - q^{-5} + q^{-6} </math> \|
	coloured_jones_4 = <math>q^{88}-3 q^{87}+2 q^{86}+3 q^{85}-5 q^{84}+5 q^{83}-12 q^{82}+9 q^{81}+15 q^{80}-20 q^{79}+13 q^{78}-42 q^{77}+29 q^{76}+59 q^{75}-51 q^{74}+6 q^{73}-121 q^{72}+81 q^{71}+183 q^{70}-73 q^{69}-52 q^{68}-333 q^{67}+140 q^{66}+461 q^{65}+18 q^{64}-150 q^{63}-756 q^{62}+94 q^{61}+847 q^{60}+315 q^{59}-159 q^{58}-1309 q^{57}-150 q^{56}+1158 q^{55}+738 q^{54}+10 q^{53}-1762 q^{52}-506 q^{51}+1238 q^{50}+1084 q^{49}+306 q^{48}-1951 q^{47}-809 q^{46}+1093 q^{45}+1230 q^{44}+604 q^{43}-1861 q^{42}-982 q^{41}+795 q^{40}+1189 q^{39}+850 q^{38}-1557 q^{37}-1040 q^{36}+410 q^{35}+1004 q^{34}+1021 q^{33}-1094 q^{32}-976 q^{31}-3 q^{30}+692 q^{29}+1062 q^{28}-562 q^{27}-756 q^{26}-311 q^{25}+301 q^{24}+895 q^{23}-119 q^{22}-412 q^{21}-387 q^{20}-25 q^{19}+561 q^{18}+88 q^{17}-102 q^{16}-255 q^{15}-151 q^{14}+238 q^{13}+83 q^{12}+40 q^{11}-92 q^{10}-113 q^9+67 q^8+19 q^7+43 q^6-13 q^5-45 q^4+18 q^3-8 q^2+16 q+2-13 q^{-1} +9 q^{-2} -6 q^{-3} +3 q^{-4} + q^{-5} -4 q^{-6} +4 q^{-7} - q^{-8} - q^{-11} + q^{-12} </math> \|		coloured_jones_4 = <math>q^{88}-3 q^{87}+2 q^{86}+3 q^{85}-5 q^{84}+5 q^{83}-12 q^{82}+9 q^{81}+15 q^{80}-20 q^{79}+13 q^{78}-42 q^{77}+29 q^{76}+59 q^{75}-51 q^{74}+6 q^{73}-121 q^{72}+81 q^{71}+183 q^{70}-73 q^{69}-52 q^{68}-333 q^{67}+140 q^{66}+461 q^{65}+18 q^{64}-150 q^{63}-756 q^{62}+94 q^{61}+847 q^{60}+315 q^{59}-159 q^{58}-1309 q^{57}-150 q^{56}+1158 q^{55}+738 q^{54}+10 q^{53}-1762 q^{52}-506 q^{51}+1238 q^{50}+1084 q^{49}+306 q^{48}-1951 q^{47}-809 q^{46}+1093 q^{45}+1230 q^{44}+604 q^{43}-1861 q^{42}-982 q^{41}+795 q^{40}+1189 q^{39}+850 q^{38}-1557 q^{37}-1040 q^{36}+410 q^{35}+1004 q^{34}+1021 q^{33}-1094 q^{32}-976 q^{31}-3 q^{30}+692 q^{29}+1062 q^{28}-562 q^{27}-756 q^{26}-311 q^{25}+301 q^{24}+895 q^{23}-119 q^{22}-412 q^{21}-387 q^{20}-25 q^{19}+561 q^{18}+88 q^{17}-102 q^{16}-255 q^{15}-151 q^{14}+238 q^{13}+83 q^{12}+40 q^{11}-92 q^{10}-113 q^9+67 q^8+19 q^7+43 q^6-13 q^5-45 q^4+18 q^3-8 q^2+16 q+2-13 q^{-1} +9 q^{-2} -6 q^{-3} +3 q^{-4} + q^{-5} -4 q^{-6} +4 q^{-7} - q^{-8} - 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>
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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, 76]]</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, 76]]</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[14, 10, 15, 9], X[12, 3, 13, 4], X[2, 13, 3, 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[4, 2, 5, 1], X[14, 10, 15, 9], X[12, 3, 13, 4], X[2, 13, 3, 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>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, 76]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_76_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, 76]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_76_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, 76]]&) /@ {~~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, 76]]&) /@ {
			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, 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, 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, 76]][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, 76]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:40, 30 August 2005

2005-08-30T14:40:49Z

Show changes

DrorsRobot at 01:08, 30 August 2005

2005-08-30T01:08:36Z

← Older revision		Revision as of 21:08, 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 22:19, 29 August 2005

2005-08-29T22:19:42Z

Show changes

ScottTestRobot at 00:14, 29 August 2005

2005-08-29T00:14:52Z

← Older revision		Revision as of 20:14, 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=76\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-1,5,-7,6,-8,2,-10,9,-3,4,-2,10,-9,8,-5,7,-6/goTop.html}}
	{\| align=left
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=76\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-1,5,-7,6,-8,2,-10,9,-3,4,-2,10,-9,8,-5,7,-6/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>1</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>		<tr align=center><td>1</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</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}}

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	4 q t + q t + 2 q t + q t</nowiki></pre></td></tr>		4 q t + q t + 2 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:51, 28 August 2005

2005-08-28T01:51:20Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:26Z

Resetting knot page to basic template.

New page

10 76 - Revision history

ScottTestRobot at 22:04, 1 September 2005

DrorsRobot at 22:53, 31 August 2005

ScottKnotPageRobot at 14:40, 30 August 2005

DrorsRobot at 01:08, 30 August 2005

DrorsRobot at 22:19, 29 August 2005

ScottTestRobot at 00:14, 29 August 2005

ScottTestRobot at 01:51, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.