ScottTestRobot at 22:00, 1 September 2005

2005-09-01T22:00:30Z

DrorsRobot at 22:45, 31 August 2005

2005-08-31T22:45:16Z

← Older revision		Revision as of 18:45, 31 August 2005
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	{{Rolfsen Knot Page\|		{{Rolfsen Knot Page\|
	n = 10 \|		n = 10 \|
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	coloured_jones_3 = <math>-q^{45}+2 q^{44}-q^{43}-q^{42}-q^{41}+7 q^{40}-3 q^{39}-10 q^{38}+q^{37}+27 q^{36}-5 q^{35}-42 q^{34}-11 q^{33}+78 q^{32}+25 q^{31}-105 q^{30}-66 q^{29}+136 q^{28}+119 q^{27}-159 q^{26}-179 q^{25}+164 q^{24}+252 q^{23}-166 q^{22}-307 q^{21}+140 q^{20}+371 q^{19}-127 q^{18}-399 q^{17}+84 q^{16}+429 q^{15}-59 q^{14}-418 q^{13}+11 q^{12}+405 q^{11}+24 q^{10}-360 q^9-64 q^8+308 q^7+88 q^6-237 q^5-110 q^4+178 q^3+105 q^2-112 q-98+69 q^{-1} +75 q^{-2} -34 q^{-3} -55 q^{-4} +16 q^{-5} +35 q^{-6} -6 q^{-7} -21 q^{-8} +2 q^{-9} +11 q^{-10} - q^{-11} -4 q^{-12} - q^{-13} +3 q^{-14} - q^{-15} </math> \|		coloured_jones_3 = <math>-q^{45}+2 q^{44}-q^{43}-q^{42}-q^{41}+7 q^{40}-3 q^{39}-10 q^{38}+q^{37}+27 q^{36}-5 q^{35}-42 q^{34}-11 q^{33}+78 q^{32}+25 q^{31}-105 q^{30}-66 q^{29}+136 q^{28}+119 q^{27}-159 q^{26}-179 q^{25}+164 q^{24}+252 q^{23}-166 q^{22}-307 q^{21}+140 q^{20}+371 q^{19}-127 q^{18}-399 q^{17}+84 q^{16}+429 q^{15}-59 q^{14}-418 q^{13}+11 q^{12}+405 q^{11}+24 q^{10}-360 q^9-64 q^8+308 q^7+88 q^6-237 q^5-110 q^4+178 q^3+105 q^2-112 q-98+69 q^{-1} +75 q^{-2} -34 q^{-3} -55 q^{-4} +16 q^{-5} +35 q^{-6} -6 q^{-7} -21 q^{-8} +2 q^{-9} +11 q^{-10} - q^{-11} -4 q^{-12} - q^{-13} +3 q^{-14} - q^{-15} </math> \|
	coloured_jones_4 = <math>q^{74}-2 q^{73}+q^{72}+q^{71}-3 q^{70}+5 q^{69}-7 q^{68}+5 q^{67}+6 q^{66}-16 q^{65}+11 q^{64}-18 q^{63}+24 q^{62}+32 q^{61}-49 q^{60}-4 q^{59}-66 q^{58}+71 q^{57}+133 q^{56}-56 q^{55}-51 q^{54}-251 q^{53}+66 q^{52}+340 q^{51}+94 q^{50}-11 q^{49}-608 q^{48}-164 q^{47}+499 q^{46}+446 q^{45}+328 q^{44}-963 q^{43}-673 q^{42}+384 q^{41}+829 q^{40}+981 q^{39}-1082 q^{38}-1251 q^{37}-34 q^{36}+1020 q^{35}+1716 q^{34}-929 q^{33}-1660 q^{32}-555 q^{31}+979 q^{30}+2277 q^{29}-639 q^{28}-1812 q^{27}-987 q^{26}+779 q^{25}+2557 q^{24}-309 q^{23}-1718 q^{22}-1269 q^{21}+454 q^{20}+2525 q^{19}+57 q^{18}-1372 q^{17}-1390 q^{16}+15 q^{15}+2164 q^{14}+398 q^{13}-802 q^{12}-1265 q^{11}-424 q^{10}+1504 q^9+554 q^8-183 q^7-881 q^6-649 q^5+776 q^4+435 q^3+204 q^2-410 q-559+266 q^{-1} +184 q^{-2} +264 q^{-3} -95 q^{-4} -319 q^{-5} +61 q^{-6} +17 q^{-7} +158 q^{-8} +10 q^{-9} -134 q^{-10} +20 q^{-11} -22 q^{-12} +62 q^{-13} +14 q^{-14} -47 q^{-15} +12 q^{-16} -13 q^{-17} +18 q^{-18} +6 q^{-19} -14 q^{-20} +4 q^{-21} -3 q^{-22} +4 q^{-23} + q^{-24} -3 q^{-25} + q^{-26} </math> \|		coloured_jones_4 = <math>q^{74}-2 q^{73}+q^{72}+q^{71}-3 q^{70}+5 q^{69}-7 q^{68}+5 q^{67}+6 q^{66}-16 q^{65}+11 q^{64}-18 q^{63}+24 q^{62}+32 q^{61}-49 q^{60}-4 q^{59}-66 q^{58}+71 q^{57}+133 q^{56}-56 q^{55}-51 q^{54}-251 q^{53}+66 q^{52}+340 q^{51}+94 q^{50}-11 q^{49}-608 q^{48}-164 q^{47}+499 q^{46}+446 q^{45}+328 q^{44}-963 q^{43}-673 q^{42}+384 q^{41}+829 q^{40}+981 q^{39}-1082 q^{38}-1251 q^{37}-34 q^{36}+1020 q^{35}+1716 q^{34}-929 q^{33}-1660 q^{32}-555 q^{31}+979 q^{30}+2277 q^{29}-639 q^{28}-1812 q^{27}-987 q^{26}+779 q^{25}+2557 q^{24}-309 q^{23}-1718 q^{22}-1269 q^{21}+454 q^{20}+2525 q^{19}+57 q^{18}-1372 q^{17}-1390 q^{16}+15 q^{15}+2164 q^{14}+398 q^{13}-802 q^{12}-1265 q^{11}-424 q^{10}+1504 q^9+554 q^8-183 q^7-881 q^6-649 q^5+776 q^4+435 q^3+204 q^2-410 q-559+266 q^{-1} +184 q^{-2} +264 q^{-3} -95 q^{-4} -319 q^{-5} +61 q^{-6} +17 q^{-7} +158 q^{-8} +10 q^{-9} -134 q^{-10} +20 q^{-11} -22 q^{-12} +62 q^{-13} +14 q^{-14} -47 q^{-15} +12 q^{-16} -13 q^{-17} +18 q^{-18} +6 q^{-19} -14 q^{-20} +4 q^{-21} -3 q^{-22} +4 q^{-23} + q^{-24} -3 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, 65]]</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, 65]]</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[1, 4, 2, 5], X[3, 10, 4, 11], X[11, 19, 12, 18], X[5, 15, 6, 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[1, 4, 2, 5], X[3, 10, 4, 11], X[11, 19, 12, 18], X[5, 15, 6, 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, 65]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_65_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, 65]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_65_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, 65]]&) /@ {~~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, 65]]&) /@ {
			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, 65]][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, 65]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:36, 30 August 2005

2005-08-30T14:36:24Z

Show changes

DrorsRobot at 01:03, 30 August 2005

2005-08-30T01:03:40Z

← Older revision		Revision as of 21:03, 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 22:18, 29 August 2005

2005-08-29T22:18:37Z

Show changes

ScottTestRobot at 00:09, 29 August 2005

2005-08-29T00:09:30Z

← Older revision		Revision as of 20:09, 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=65\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,5,-6,7,-10,2,-3,9,-8,4,-7,6,-5,3,-9,8/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=65\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,5,-6,7,-10,2,-3,9,-8,4,-7,6,-5,3,-9,8/goTop.html}}
	\|{{:{{PAGENAME}} Quick Notes}}
	\|}

	<br style="clear:both" />		<br style="clear:both" />
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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>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr>		<tr align=center><td>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</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> </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> </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 + q t + q t</nowiki></pre></td></tr>		4 q t + q t + q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:46, 28 August 2005

2005-08-28T01:46:48Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:16Z

Resetting knot page to basic template.

New page

10 65 - Revision history

ScottTestRobot at 22:00, 1 September 2005

DrorsRobot at 22:45, 31 August 2005

ScottKnotPageRobot at 14:36, 30 August 2005

DrorsRobot at 01:03, 30 August 2005

DrorsRobot at 22:18, 29 August 2005

ScottTestRobot at 00:09, 29 August 2005

ScottTestRobot at 01:46, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.