10 83 - Revision history

Drorbn: Reverted edits by DartrOcrel (Talk); changed back to last version by ScottTestRobot

2009-05-28T03:25:42Z

Reverted edits by DartrOcrel (Talk); changed back to last version by ScottTestRobot

← Older revision		Revision as of 23:25, 27 May 2009
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	http://www.textletoacelouli.com
	<!-- WARNING! WARNING! WARNING!		<!-- WARNING! WARNING! WARNING!
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DartrOcrel at 18:59, 22 May 2009

2009-05-22T18:59:16Z

← Older revision		Revision as of 14:59, 22 May 2009
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			http://www.textletoacelouli.com
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ScottTestRobot at 22:05, 1 September 2005

2005-09-01T22:05:49Z

Show changes

DrorsRobot at 22:54, 31 August 2005

2005-08-31T22:54:39Z

← Older revision		Revision as of 18:54, 31 August 2005
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			<!-- WARNING! WARNING! WARNING!
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	<!-- --> <!--
			<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)
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			<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Rolfsen_Splice_Base]]. -->
			<!-- <math>\text{Null}</math> -->
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	{{Rolfsen Knot Page\|		{{Rolfsen Knot Page\|
	n = 10 \|		n = 10 \|
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	coloured_jones_3 = <math>-q^{45}+3 q^{44}-2 q^{43}-3 q^{42}+2 q^{41}+11 q^{40}-9 q^{39}-24 q^{38}+17 q^{37}+54 q^{36}-25 q^{35}-105 q^{34}+16 q^{33}+184 q^{32}+20 q^{31}-279 q^{30}-97 q^{29}+372 q^{28}+226 q^{27}-457 q^{26}-378 q^{25}+498 q^{24}+555 q^{23}-507 q^{22}-725 q^{21}+481 q^{20}+867 q^{19}-422 q^{18}-972 q^{17}+339 q^{16}+1036 q^{15}-243 q^{14}-1047 q^{13}+129 q^{12}+1015 q^{11}-18 q^{10}-925 q^9-100 q^8+806 q^7+184 q^6-640 q^5-251 q^4+481 q^3+255 q^2-308 q-243+186 q^{-1} +186 q^{-2} -88 q^{-3} -132 q^{-4} +39 q^{-5} +76 q^{-6} -8 q^{-7} -45 q^{-8} +4 q^{-9} +19 q^{-10} -7 q^{-12} -2 q^{-13} +4 q^{-14} - q^{-15} </math> \|		coloured_jones_3 = <math>-q^{45}+3 q^{44}-2 q^{43}-3 q^{42}+2 q^{41}+11 q^{40}-9 q^{39}-24 q^{38}+17 q^{37}+54 q^{36}-25 q^{35}-105 q^{34}+16 q^{33}+184 q^{32}+20 q^{31}-279 q^{30}-97 q^{29}+372 q^{28}+226 q^{27}-457 q^{26}-378 q^{25}+498 q^{24}+555 q^{23}-507 q^{22}-725 q^{21}+481 q^{20}+867 q^{19}-422 q^{18}-972 q^{17}+339 q^{16}+1036 q^{15}-243 q^{14}-1047 q^{13}+129 q^{12}+1015 q^{11}-18 q^{10}-925 q^9-100 q^8+806 q^7+184 q^6-640 q^5-251 q^4+481 q^3+255 q^2-308 q-243+186 q^{-1} +186 q^{-2} -88 q^{-3} -132 q^{-4} +39 q^{-5} +76 q^{-6} -8 q^{-7} -45 q^{-8} +4 q^{-9} +19 q^{-10} -7 q^{-12} -2 q^{-13} +4 q^{-14} - q^{-15} </math> \|
	coloured_jones_4 = <math>q^{74}-3 q^{73}+2 q^{72}+3 q^{71}-6 q^{70}+5 q^{69}-10 q^{68}+15 q^{67}+14 q^{66}-41 q^{65}+4 q^{64}-23 q^{63}+81 q^{62}+83 q^{61}-145 q^{60}-91 q^{59}-127 q^{58}+270 q^{57}+411 q^{56}-196 q^{55}-390 q^{54}-670 q^{53}+370 q^{52}+1205 q^{51}+313 q^{50}-577 q^{49}-1952 q^{48}-303 q^{47}+2055 q^{46}+1750 q^{45}+188 q^{44}-3487 q^{43}-2140 q^{42}+2023 q^{41}+3557 q^{40}+2245 q^{39}-4266 q^{38}-4474 q^{37}+760 q^{36}+4730 q^{35}+4842 q^{34}-3919 q^{33}-6263 q^{32}-1085 q^{31}+4893 q^{30}+6944 q^{29}-2870 q^{28}-7048 q^{27}-2771 q^{26}+4292 q^{25}+8120 q^{24}-1549 q^{23}-6895 q^{22}-4044 q^{21}+3122 q^{20}+8329 q^{19}-40 q^{18}-5817 q^{17}-4833 q^{16}+1397 q^{15}+7463 q^{14}+1463 q^{13}-3823 q^{12}-4793 q^{11}-530 q^{10}+5457 q^9+2331 q^8-1433 q^7-3648 q^6-1787 q^5+2909 q^4+2051 q^3+296 q^2-1883 q-1794+940 q^{-1} +1045 q^{-2} +770 q^{-3} -530 q^{-4} -1028 q^{-5} +117 q^{-6} +245 q^{-7} +472 q^{-8} -19 q^{-9} -371 q^{-10} -3 q^{-11} -13 q^{-12} +160 q^{-13} +30 q^{-14} -101 q^{-15} +10 q^{-16} -20 q^{-17} +38 q^{-18} +10 q^{-19} -24 q^{-20} +4 q^{-21} -5 q^{-22} +7 q^{-23} +2 q^{-24} -4 q^{-25} + q^{-26} </math> \|		coloured_jones_4 = <math>q^{74}-3 q^{73}+2 q^{72}+3 q^{71}-6 q^{70}+5 q^{69}-10 q^{68}+15 q^{67}+14 q^{66}-41 q^{65}+4 q^{64}-23 q^{63}+81 q^{62}+83 q^{61}-145 q^{60}-91 q^{59}-127 q^{58}+270 q^{57}+411 q^{56}-196 q^{55}-390 q^{54}-670 q^{53}+370 q^{52}+1205 q^{51}+313 q^{50}-577 q^{49}-1952 q^{48}-303 q^{47}+2055 q^{46}+1750 q^{45}+188 q^{44}-3487 q^{43}-2140 q^{42}+2023 q^{41}+3557 q^{40}+2245 q^{39}-4266 q^{38}-4474 q^{37}+760 q^{36}+4730 q^{35}+4842 q^{34}-3919 q^{33}-6263 q^{32}-1085 q^{31}+4893 q^{30}+6944 q^{29}-2870 q^{28}-7048 q^{27}-2771 q^{26}+4292 q^{25}+8120 q^{24}-1549 q^{23}-6895 q^{22}-4044 q^{21}+3122 q^{20}+8329 q^{19}-40 q^{18}-5817 q^{17}-4833 q^{16}+1397 q^{15}+7463 q^{14}+1463 q^{13}-3823 q^{12}-4793 q^{11}-530 q^{10}+5457 q^9+2331 q^8-1433 q^7-3648 q^6-1787 q^5+2909 q^4+2051 q^3+296 q^2-1883 q-1794+940 q^{-1} +1045 q^{-2} +770 q^{-3} -530 q^{-4} -1028 q^{-5} +117 q^{-6} +245 q^{-7} +472 q^{-8} -19 q^{-9} -371 q^{-10} -3 q^{-11} -13 q^{-12} +160 q^{-13} +30 q^{-14} -101 q^{-15} +10 q^{-16} -20 q^{-17} +38 q^{-18} +10 q^{-19} -24 q^{-20} +4 q^{-21} -5 q^{-22} +7 q^{-23} +2 q^{-24} -4 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, 83]]</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, 83]]</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, 6, 2, 7], X[5, 16, 6, 17], X[13, 1, 14, 20], X[7, 15, 8, 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, 6, 2, 7], X[5, 16, 6, 17], X[13, 1, 14, 20], X[7, 15, 8, 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, 83]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_83_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, 83]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_83_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, 83]]&) /@ {~~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, 83]]&) /@ {
			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>{Chiral, 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>{Chiral, 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, 83]][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, 83]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:41, 30 August 2005

2005-08-30T14:41:50Z

Show changes

DrorsRobot at 01:09, 30 August 2005

2005-08-30T01:09:54Z

← Older revision		Revision as of 21:09, 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 22:20, 29 August 2005

2005-08-29T22:20:23Z

Show changes

ScottTestRobot at 00:16, 29 August 2005

2005-08-29T00:16:24Z

← Older revision		Revision as of 20:16, 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=83\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-5,6,-2,1,-4,5,-6,7,-8,9,-3,4,-10,2,-9,8,-7,3/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=83\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-5,6,-2,1,-4,5,-6,7,-8,9,-3,4,-10,2,-9,8,-7,3/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>
	<tr align=center>		<tr align=center>
	<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>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>3</td></tr>		<tr align=center><td>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>3</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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	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 01:52, 28 August 2005

2005-08-28T01:52:39Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:32Z

Resetting knot page to basic template.

New page