ScottTestRobot at 21:58, 1 September 2005

2005-09-01T21:58:34Z

DrorsRobot at 22:42, 31 August 2005

2005-08-31T22:42:27Z

← Older revision		Revision as of 18:42, 31 August 2005
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	coloured_jones_3 = <math>q^{36}-3 q^{35}+q^{34}+5 q^{33}+3 q^{32}-19 q^{31}-9 q^{30}+40 q^{29}+36 q^{28}-72 q^{27}-92 q^{26}+93 q^{25}+199 q^{24}-98 q^{23}-332 q^{22}+36 q^{21}+501 q^{20}+83 q^{19}-654 q^{18}-273 q^{17}+772 q^{16}+511 q^{15}-833 q^{14}-771 q^{13}+831 q^{12}+1023 q^{11}-773 q^{10}-1241 q^9+662 q^8+1424 q^7-532 q^6-1532 q^5+365 q^4+1583 q^3-191 q^2-1554 q+20+1437 q^{-1} +143 q^{-2} -1259 q^{-3} -249 q^{-4} +1004 q^{-5} +324 q^{-6} -754 q^{-7} -314 q^{-8} +497 q^{-9} +279 q^{-10} -309 q^{-11} -194 q^{-12} +158 q^{-13} +129 q^{-14} -79 q^{-15} -70 q^{-16} +37 q^{-17} +29 q^{-18} -13 q^{-19} -11 q^{-20} +4 q^{-21} +5 q^{-22} -4 q^{-23} + q^{-24} </math> \|		coloured_jones_3 = <math>q^{36}-3 q^{35}+q^{34}+5 q^{33}+3 q^{32}-19 q^{31}-9 q^{30}+40 q^{29}+36 q^{28}-72 q^{27}-92 q^{26}+93 q^{25}+199 q^{24}-98 q^{23}-332 q^{22}+36 q^{21}+501 q^{20}+83 q^{19}-654 q^{18}-273 q^{17}+772 q^{16}+511 q^{15}-833 q^{14}-771 q^{13}+831 q^{12}+1023 q^{11}-773 q^{10}-1241 q^9+662 q^8+1424 q^7-532 q^6-1532 q^5+365 q^4+1583 q^3-191 q^2-1554 q+20+1437 q^{-1} +143 q^{-2} -1259 q^{-3} -249 q^{-4} +1004 q^{-5} +324 q^{-6} -754 q^{-7} -314 q^{-8} +497 q^{-9} +279 q^{-10} -309 q^{-11} -194 q^{-12} +158 q^{-13} +129 q^{-14} -79 q^{-15} -70 q^{-16} +37 q^{-17} +29 q^{-18} -13 q^{-19} -11 q^{-20} +4 q^{-21} +5 q^{-22} -4 q^{-23} + q^{-24} </math> \|
	coloured_jones_4 = <math>q^{60}-3 q^{59}+q^{58}+5 q^{57}-3 q^{56}+3 q^{55}-22 q^{54}+3 q^{53}+42 q^{52}+8 q^{51}+10 q^{50}-132 q^{49}-61 q^{48}+153 q^{47}+168 q^{46}+183 q^{45}-413 q^{44}-486 q^{43}+78 q^{42}+568 q^{41}+1058 q^{40}-438 q^{39}-1427 q^{38}-943 q^{37}+527 q^{36}+2848 q^{35}+825 q^{34}-1960 q^{33}-3151 q^{32}-1252 q^{31}+4417 q^{30}+3623 q^{29}-588 q^{28}-5259 q^{27}-4968 q^{26}+4120 q^{25}+6571 q^{24}+2914 q^{23}-5652 q^{22}-9164 q^{21}+1697 q^{20}+8110 q^{19}+7178 q^{18}-4118 q^{17}-12277 q^{16}-1705 q^{15}+7965 q^{14}+10792 q^{13}-1582 q^{12}-13811 q^{11}-4977 q^{10}+6672 q^9+13171 q^8+1213 q^7-13785 q^6-7654 q^5+4493 q^4+14001 q^3+3978 q^2-11969 q-9232+1487 q^{-1} +12686 q^{-2} +6116 q^{-3} -8311 q^{-4} -8871 q^{-5} -1544 q^{-6} +9152 q^{-7} +6528 q^{-8} -3997 q^{-9} -6376 q^{-10} -3110 q^{-11} +4797 q^{-12} +4894 q^{-13} -928 q^{-14} -3140 q^{-15} -2690 q^{-16} +1643 q^{-17} +2500 q^{-18} +161 q^{-19} -928 q^{-20} -1399 q^{-21} +326 q^{-22} +852 q^{-23} +157 q^{-24} -116 q^{-25} -467 q^{-26} +45 q^{-27} +198 q^{-28} +23 q^{-29} +16 q^{-30} -105 q^{-31} +11 q^{-32} +36 q^{-33} -7 q^{-34} +7 q^{-35} -15 q^{-36} +4 q^{-37} +5 q^{-38} -4 q^{-39} + q^{-40} </math> \|		coloured_jones_4 = <math>q^{60}-3 q^{59}+q^{58}+5 q^{57}-3 q^{56}+3 q^{55}-22 q^{54}+3 q^{53}+42 q^{52}+8 q^{51}+10 q^{50}-132 q^{49}-61 q^{48}+153 q^{47}+168 q^{46}+183 q^{45}-413 q^{44}-486 q^{43}+78 q^{42}+568 q^{41}+1058 q^{40}-438 q^{39}-1427 q^{38}-943 q^{37}+527 q^{36}+2848 q^{35}+825 q^{34}-1960 q^{33}-3151 q^{32}-1252 q^{31}+4417 q^{30}+3623 q^{29}-588 q^{28}-5259 q^{27}-4968 q^{26}+4120 q^{25}+6571 q^{24}+2914 q^{23}-5652 q^{22}-9164 q^{21}+1697 q^{20}+8110 q^{19}+7178 q^{18}-4118 q^{17}-12277 q^{16}-1705 q^{15}+7965 q^{14}+10792 q^{13}-1582 q^{12}-13811 q^{11}-4977 q^{10}+6672 q^9+13171 q^8+1213 q^7-13785 q^6-7654 q^5+4493 q^4+14001 q^3+3978 q^2-11969 q-9232+1487 q^{-1} +12686 q^{-2} +6116 q^{-3} -8311 q^{-4} -8871 q^{-5} -1544 q^{-6} +9152 q^{-7} +6528 q^{-8} -3997 q^{-9} -6376 q^{-10} -3110 q^{-11} +4797 q^{-12} +4894 q^{-13} -928 q^{-14} -3140 q^{-15} -2690 q^{-16} +1643 q^{-17} +2500 q^{-18} +161 q^{-19} -928 q^{-20} -1399 q^{-21} +326 q^{-22} +852 q^{-23} +157 q^{-24} -116 q^{-25} -467 q^{-26} +45 q^{-27} +198 q^{-28} +23 q^{-29} +16 q^{-30} -105 q^{-31} +11 q^{-32} +36 q^{-33} -7 q^{-34} +7 q^{-35} -15 q^{-36} +4 q^{-37} +5 q^{-38} -4 q^{-39} + q^{-40} </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, 96]]</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, 96]]</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[5, 18, 6, 19], X[3, 9, 4, 8], X[9, 3, 10, 2],		<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[5, 18, 6, 19], X[3, 9, 4, 8], X[9, 3, 10, 2],
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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>5</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>5</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, 96]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_96_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, 96]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_96_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, 96]]&) /@ {~~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, 96]]&) /@ {
			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, 96]][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, 96]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:34, 30 August 2005

2005-08-30T14:34:29Z

Show changes

DrorsRobot at 01:01, 30 August 2005

2005-08-30T01:01:30Z

← 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

2005-08-29T22:01:28Z

Show changes

ScottTestRobot at 00:07, 29 August 2005

2005-08-29T00:07:09Z

← 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=96\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,7,-6,3,-4,8,-5,6,-9,10,-7,5,-8,2,-10,9/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=96\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,7,-6,3,-4,8,-5,6,-9,10,-7,5,-8,2,-10,9/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>-7</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>-7</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>-9</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>-9</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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	q t + 2 q t + q t</nowiki></pre></td></tr>		q t + 2 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:45, 28 August 2005

2005-08-28T01:45:24Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:44Z

Resetting knot page to basic template.

New page

10 96 - 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.