ScottTestRobot at 21:58, 1 September 2005

2005-09-01T21:58:43Z

DrorsRobot at 22:42, 31 August 2005

2005-08-31T22:42:40Z

← Older revision		Revision as of 18:42, 31 August 2005
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	{{Rolfsen Knot Page\|		{{Rolfsen Knot Page\|
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	coloured_jones_3 = <math>q^{54}-4 q^{53}+3 q^{52}+6 q^{51}-4 q^{50}-16 q^{49}+7 q^{48}+40 q^{47}-21 q^{46}-69 q^{45}+25 q^{44}+128 q^{43}-33 q^{42}-202 q^{41}+22 q^{40}+302 q^{39}-2 q^{38}-401 q^{37}-46 q^{36}+502 q^{35}+108 q^{34}-583 q^{33}-179 q^{32}+633 q^{31}+256 q^{30}-656 q^{29}-321 q^{28}+636 q^{27}+385 q^{26}-596 q^{25}-424 q^{24}+521 q^{23}+454 q^{22}-434 q^{21}-456 q^{20}+325 q^{19}+446 q^{18}-227 q^{17}-399 q^{16}+123 q^{15}+344 q^{14}-48 q^{13}-266 q^{12}-11 q^{11}+196 q^{10}+33 q^9-120 q^8-48 q^7+76 q^6+34 q^5-34 q^4-28 q^3+19 q^2+13 q-5-9 q^{-1} +4 q^{-2} +2 q^{-3} -2 q^{-5} + q^{-6} </math> \|		coloured_jones_3 = <math>q^{54}-4 q^{53}+3 q^{52}+6 q^{51}-4 q^{50}-16 q^{49}+7 q^{48}+40 q^{47}-21 q^{46}-69 q^{45}+25 q^{44}+128 q^{43}-33 q^{42}-202 q^{41}+22 q^{40}+302 q^{39}-2 q^{38}-401 q^{37}-46 q^{36}+502 q^{35}+108 q^{34}-583 q^{33}-179 q^{32}+633 q^{31}+256 q^{30}-656 q^{29}-321 q^{28}+636 q^{27}+385 q^{26}-596 q^{25}-424 q^{24}+521 q^{23}+454 q^{22}-434 q^{21}-456 q^{20}+325 q^{19}+446 q^{18}-227 q^{17}-399 q^{16}+123 q^{15}+344 q^{14}-48 q^{13}-266 q^{12}-11 q^{11}+196 q^{10}+33 q^9-120 q^8-48 q^7+76 q^6+34 q^5-34 q^4-28 q^3+19 q^2+13 q-5-9 q^{-1} +4 q^{-2} +2 q^{-3} -2 q^{-5} + q^{-6} </math> \|
	coloured_jones_4 = <math>q^{88}-4 q^{87}+3 q^{86}+6 q^{85}-8 q^{84}+4 q^{83}-19 q^{82}+20 q^{81}+30 q^{80}-43 q^{79}+5 q^{78}-66 q^{77}+88 q^{76}+123 q^{75}-141 q^{74}-63 q^{73}-198 q^{72}+283 q^{71}+415 q^{70}-277 q^{69}-329 q^{68}-594 q^{67}+601 q^{66}+1106 q^{65}-242 q^{64}-825 q^{63}-1476 q^{62}+812 q^{61}+2180 q^{60}+243 q^{59}-1271 q^{58}-2792 q^{57}+602 q^{56}+3244 q^{55}+1154 q^{54}-1309 q^{53}-4078 q^{52}-41 q^{51}+3815 q^{50}+2111 q^{49}-861 q^{48}-4849 q^{47}-833 q^{46}+3734 q^{45}+2753 q^{44}-135 q^{43}-4939 q^{42}-1515 q^{41}+3113 q^{40}+2985 q^{39}+673 q^{38}-4435 q^{37}-2005 q^{36}+2126 q^{35}+2837 q^{34}+1433 q^{33}-3449 q^{32}-2228 q^{31}+946 q^{30}+2299 q^{29}+1960 q^{28}-2149 q^{27}-2035 q^{26}-113 q^{25}+1420 q^{24}+1994 q^{23}-879 q^{22}-1400 q^{21}-686 q^{20}+495 q^{19}+1496 q^{18}-61 q^{17}-624 q^{16}-667 q^{15}-83 q^{14}+791 q^{13}+182 q^{12}-104 q^{11}-358 q^{10}-214 q^9+285 q^8+112 q^7+57 q^6-112 q^5-127 q^4+73 q^3+25 q^2+43 q-19-44 q^{-1} +18 q^{-2} - q^{-3} +13 q^{-4} - q^{-5} -11 q^{-6} +5 q^{-7} - q^{-8} +2 q^{-9} -2 q^{-11} + q^{-12} </math> \|		coloured_jones_4 = <math>q^{88}-4 q^{87}+3 q^{86}+6 q^{85}-8 q^{84}+4 q^{83}-19 q^{82}+20 q^{81}+30 q^{80}-43 q^{79}+5 q^{78}-66 q^{77}+88 q^{76}+123 q^{75}-141 q^{74}-63 q^{73}-198 q^{72}+283 q^{71}+415 q^{70}-277 q^{69}-329 q^{68}-594 q^{67}+601 q^{66}+1106 q^{65}-242 q^{64}-825 q^{63}-1476 q^{62}+812 q^{61}+2180 q^{60}+243 q^{59}-1271 q^{58}-2792 q^{57}+602 q^{56}+3244 q^{55}+1154 q^{54}-1309 q^{53}-4078 q^{52}-41 q^{51}+3815 q^{50}+2111 q^{49}-861 q^{48}-4849 q^{47}-833 q^{46}+3734 q^{45}+2753 q^{44}-135 q^{43}-4939 q^{42}-1515 q^{41}+3113 q^{40}+2985 q^{39}+673 q^{38}-4435 q^{37}-2005 q^{36}+2126 q^{35}+2837 q^{34}+1433 q^{33}-3449 q^{32}-2228 q^{31}+946 q^{30}+2299 q^{29}+1960 q^{28}-2149 q^{27}-2035 q^{26}-113 q^{25}+1420 q^{24}+1994 q^{23}-879 q^{22}-1400 q^{21}-686 q^{20}+495 q^{19}+1496 q^{18}-61 q^{17}-624 q^{16}-667 q^{15}-83 q^{14}+791 q^{13}+182 q^{12}-104 q^{11}-358 q^{10}-214 q^9+285 q^8+112 q^7+57 q^6-112 q^5-127 q^4+73 q^3+25 q^2+43 q-19-44 q^{-1} +18 q^{-2} - q^{-3} +13 q^{-4} - q^{-5} -11 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>
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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, 72]]</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, 72]]</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, 6, 11, 5], X[8, 3, 9, 4], X[2, 9, 3, 10],		<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, 6, 11, 5], X[8, 3, 9, 4], X[2, 9, 3, 10],
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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, 72]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_72_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, 72]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_72_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, 72]]&) /@ {~~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, 72]]&) /@ {
			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, 72]][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, 72]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:34, 30 August 2005

2005-08-30T14:34:37Z

Show changes

DrorsRobot at 01:01, 30 August 2005

2005-08-30T01:01:41Z

← Older revision		Revision as of 21:01, 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 22:01, 29 August 2005

2005-08-29T22:01:54Z

Show changes

ScottTestRobot at 00:07, 29 August 2005

2005-08-29T00:07:22Z

← Older revision		Revision as of 20:07, 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=72\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-1,2,-10,5,-3,4,-2,6,-8,7,-9,10,-5,9,-6,8,-7/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=72\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-1,2,-10,5,-3,4,-2,6,-8,7,-9,10,-5,9,-6,8,-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>
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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>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}}

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	3 q t + 4 q t + q t + 3 q t + q t</nowiki></pre></td></tr>		3 q t + 4 q t + q t + 3 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:45, 28 August 2005

2005-08-28T01:45:30Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:22Z

Resetting knot page to basic template.

New page

10 72 - Revision history

ScottTestRobot at 21:58, 1 September 2005

DrorsRobot at 22:42, 31 August 2005

ScottKnotPageRobot at 14:34, 30 August 2005

DrorsRobot at 01:01, 30 August 2005

DrorsRobot at 22:01, 29 August 2005

ScottTestRobot at 00:07, 29 August 2005

ScottTestRobot at 01:45, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.