ScottTestRobot at 22:04, 1 September 2005

2005-09-01T22:04:00Z

DrorsRobot at 22:51, 31 August 2005

2005-08-31T22:51:47Z

← Older revision		Revision as of 18:51, 31 August 2005
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	coloured_jones_3 = <math>q^{36}-3 q^{35}+5 q^{33}+6 q^{32}-15 q^{31}-16 q^{30}+26 q^{29}+42 q^{28}-36 q^{27}-86 q^{26}+32 q^{25}+152 q^{24}-10 q^{23}-227 q^{22}-46 q^{21}+303 q^{20}+140 q^{19}-377 q^{18}-249 q^{17}+414 q^{16}+391 q^{15}-434 q^{14}-525 q^{13}+414 q^{12}+662 q^{11}-377 q^{10}-773 q^9+314 q^8+854 q^7-229 q^6-917 q^5+155 q^4+912 q^3-48 q^2-899 q-9+799 q^{-1} +99 q^{-2} -705 q^{-3} -123 q^{-4} +556 q^{-5} +146 q^{-6} -423 q^{-7} -132 q^{-8} +293 q^{-9} +106 q^{-10} -189 q^{-11} -77 q^{-12} +118 q^{-13} +43 q^{-14} -61 q^{-15} -28 q^{-16} +37 q^{-17} +9 q^{-18} -16 q^{-19} -4 q^{-20} +6 q^{-21} +3 q^{-22} -4 q^{-23} + q^{-24} </math> \|		coloured_jones_3 = <math>q^{36}-3 q^{35}+5 q^{33}+6 q^{32}-15 q^{31}-16 q^{30}+26 q^{29}+42 q^{28}-36 q^{27}-86 q^{26}+32 q^{25}+152 q^{24}-10 q^{23}-227 q^{22}-46 q^{21}+303 q^{20}+140 q^{19}-377 q^{18}-249 q^{17}+414 q^{16}+391 q^{15}-434 q^{14}-525 q^{13}+414 q^{12}+662 q^{11}-377 q^{10}-773 q^9+314 q^8+854 q^7-229 q^6-917 q^5+155 q^4+912 q^3-48 q^2-899 q-9+799 q^{-1} +99 q^{-2} -705 q^{-3} -123 q^{-4} +556 q^{-5} +146 q^{-6} -423 q^{-7} -132 q^{-8} +293 q^{-9} +106 q^{-10} -189 q^{-11} -77 q^{-12} +118 q^{-13} +43 q^{-14} -61 q^{-15} -28 q^{-16} +37 q^{-17} +9 q^{-18} -16 q^{-19} -4 q^{-20} +6 q^{-21} +3 q^{-22} -4 q^{-23} + q^{-24} </math> \|
	coloured_jones_4 = <math>q^{60}-3 q^{59}+5 q^{57}+6 q^{55}-22 q^{54}-9 q^{53}+26 q^{52}+18 q^{51}+45 q^{50}-87 q^{49}-86 q^{48}+35 q^{47}+91 q^{46}+244 q^{45}-147 q^{44}-316 q^{43}-150 q^{42}+112 q^{41}+755 q^{40}+63 q^{39}-559 q^{38}-721 q^{37}-297 q^{36}+1415 q^{35}+789 q^{34}-356 q^{33}-1495 q^{32}-1430 q^{31}+1707 q^{30}+1830 q^{29}+632 q^{28}-1923 q^{27}-3065 q^{26}+1231 q^{25}+2642 q^{24}+2234 q^{23}-1640 q^{22}-4639 q^{21}+100 q^{20}+2859 q^{19}+3932 q^{18}-743 q^{17}-5712 q^{16}-1286 q^{15}+2499 q^{14}+5316 q^{13}+441 q^{12}-6159 q^{11}-2582 q^{10}+1749 q^9+6144 q^8+1648 q^7-5919 q^6-3539 q^5+725 q^4+6193 q^3+2650 q^2-4918 q-3863-403 q^{-1} +5293 q^{-2} +3115 q^{-3} -3334 q^{-4} -3346 q^{-5} -1230 q^{-6} +3676 q^{-7} +2786 q^{-8} -1747 q^{-9} -2188 q^{-10} -1401 q^{-11} +1997 q^{-12} +1880 q^{-13} -696 q^{-14} -1020 q^{-15} -1026 q^{-16} +848 q^{-17} +951 q^{-18} -246 q^{-19} -303 q^{-20} -526 q^{-21} +293 q^{-22} +359 q^{-23} -106 q^{-24} -36 q^{-25} -194 q^{-26} +92 q^{-27} +101 q^{-28} -52 q^{-29} +11 q^{-30} -50 q^{-31} +27 q^{-32} +22 q^{-33} -19 q^{-34} +4 q^{-35} -8 q^{-36} +6 q^{-37} +3 q^{-38} -4 q^{-39} + q^{-40} </math> \|		coloured_jones_4 = <math>q^{60}-3 q^{59}+5 q^{57}+6 q^{55}-22 q^{54}-9 q^{53}+26 q^{52}+18 q^{51}+45 q^{50}-87 q^{49}-86 q^{48}+35 q^{47}+91 q^{46}+244 q^{45}-147 q^{44}-316 q^{43}-150 q^{42}+112 q^{41}+755 q^{40}+63 q^{39}-559 q^{38}-721 q^{37}-297 q^{36}+1415 q^{35}+789 q^{34}-356 q^{33}-1495 q^{32}-1430 q^{31}+1707 q^{30}+1830 q^{29}+632 q^{28}-1923 q^{27}-3065 q^{26}+1231 q^{25}+2642 q^{24}+2234 q^{23}-1640 q^{22}-4639 q^{21}+100 q^{20}+2859 q^{19}+3932 q^{18}-743 q^{17}-5712 q^{16}-1286 q^{15}+2499 q^{14}+5316 q^{13}+441 q^{12}-6159 q^{11}-2582 q^{10}+1749 q^9+6144 q^8+1648 q^7-5919 q^6-3539 q^5+725 q^4+6193 q^3+2650 q^2-4918 q-3863-403 q^{-1} +5293 q^{-2} +3115 q^{-3} -3334 q^{-4} -3346 q^{-5} -1230 q^{-6} +3676 q^{-7} +2786 q^{-8} -1747 q^{-9} -2188 q^{-10} -1401 q^{-11} +1997 q^{-12} +1880 q^{-13} -696 q^{-14} -1020 q^{-15} -1026 q^{-16} +848 q^{-17} +951 q^{-18} -246 q^{-19} -303 q^{-20} -526 q^{-21} +293 q^{-22} +359 q^{-23} -106 q^{-24} -36 q^{-25} -194 q^{-26} +92 q^{-27} +101 q^{-28} -52 q^{-29} +11 q^{-30} -50 q^{-31} +27 q^{-32} +22 q^{-33} -19 q^{-34} +4 q^{-35} -8 q^{-36} +6 q^{-37} +3 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, 75]]</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, 75]]</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, 12, 6, 13], X[3, 11, 4, 10], X[11, 3, 12, 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, 12, 6, 13], X[3, 11, 4, 10], X[11, 3, 12, 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, 75]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_75_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, 75]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_75_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, 75]]&) /@ {~~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, 75]]&) /@ {
			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, 2}</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, 2}</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, 75]][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, 75]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:40, 30 August 2005

2005-08-30T14:40:05Z

Show changes

DrorsRobot at 01:07, 30 August 2005

2005-08-30T01:07:41Z

← Older revision		Revision as of 21:07, 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

2005-08-29T22:19:36Z

Show changes

ScottTestRobot at 00:13, 29 August 2005

2005-08-29T00:13:55Z

← Older revision		Revision as of 20:13, 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=75\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,7,-6,10,-9,3,-4,2,-5,6,-7,5,-8,9,-10,8/goTop.html}}
	{\| align=left
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=75\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,7,-6,10,-9,3,-4,2,-5,6,-7,5,-8,9,-10,8/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>-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 01:50, 28 August 2005

2005-08-28T01:50:26Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:25Z

Resetting knot page to basic template.

New page

10 75 - Revision history

ScottTestRobot at 22:04, 1 September 2005

DrorsRobot at 22:51, 31 August 2005

ScottKnotPageRobot at 14:40, 30 August 2005

DrorsRobot at 01:07, 30 August 2005

DrorsRobot at 22:19, 29 August 2005

ScottTestRobot at 00:13, 29 August 2005

ScottTestRobot at 01:50, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.