10 68 - Revision history

ScottTestRobot at 22:01, 1 September 2005

2005-09-01T22:01:46Z

DrorsRobot at 22:47, 31 August 2005

2005-08-31T22:47:11Z

← Older revision		Revision as of 18:47, 31 August 2005
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	coloured_jones_2 = <math>q^9-3 q^8+2 q^7+4 q^6-12 q^5+12 q^4+6 q^3-30 q^2+28 q+12-51 q^{-1} +38 q^{-2} +24 q^{-3} -64 q^{-4} +34 q^{-5} +36 q^{-6} -64 q^{-7} +19 q^{-8} +41 q^{-9} -49 q^{-10} +3 q^{-11} +36 q^{-12} -27 q^{-13} -6 q^{-14} +21 q^{-15} -9 q^{-16} -6 q^{-17} +7 q^{-18} - q^{-19} -2 q^{-20} + q^{-21} </math> \|		coloured_jones_2 = <math>q^9-3 q^8+2 q^7+4 q^6-12 q^5+12 q^4+6 q^3-30 q^2+28 q+12-51 q^{-1} +38 q^{-2} +24 q^{-3} -64 q^{-4} +34 q^{-5} +36 q^{-6} -64 q^{-7} +19 q^{-8} +41 q^{-9} -49 q^{-10} +3 q^{-11} +36 q^{-12} -27 q^{-13} -6 q^{-14} +21 q^{-15} -9 q^{-16} -6 q^{-17} +7 q^{-18} - q^{-19} -2 q^{-20} + q^{-21} </math> \|
	coloured_jones_3 = <math>-q^{18}+3 q^{17}-2 q^{16}-q^{15}+3 q^{13}-3 q^{12}-2 q^{11}+10 q^{10}-6 q^9-16 q^8+13 q^7+34 q^6-32 q^5-52 q^4+43 q^3+88 q^2-62 q-114+60 q^{-1} +153 q^{-2} -57 q^{-3} -174 q^{-4} +34 q^{-5} +192 q^{-6} -10 q^{-7} -191 q^{-8} -25 q^{-9} +185 q^{-10} +54 q^{-11} -163 q^{-12} -87 q^{-13} +144 q^{-14} +104 q^{-15} -108 q^{-16} -127 q^{-17} +80 q^{-18} +130 q^{-19} -41 q^{-20} -132 q^{-21} +11 q^{-22} +115 q^{-23} +22 q^{-24} -96 q^{-25} -40 q^{-26} +69 q^{-27} +47 q^{-28} -39 q^{-29} -47 q^{-30} +19 q^{-31} +34 q^{-32} -2 q^{-33} -24 q^{-34} -2 q^{-35} +11 q^{-36} +5 q^{-37} -6 q^{-38} -2 q^{-39} + q^{-40} +2 q^{-41} - q^{-42} </math> \|		coloured_jones_3 = <math>-q^{18}+3 q^{17}-2 q^{16}-q^{15}+3 q^{13}-3 q^{12}-2 q^{11}+10 q^{10}-6 q^9-16 q^8+13 q^7+34 q^6-32 q^5-52 q^4+43 q^3+88 q^2-62 q-114+60 q^{-1} +153 q^{-2} -57 q^{-3} -174 q^{-4} +34 q^{-5} +192 q^{-6} -10 q^{-7} -191 q^{-8} -25 q^{-9} +185 q^{-10} +54 q^{-11} -163 q^{-12} -87 q^{-13} +144 q^{-14} +104 q^{-15} -108 q^{-16} -127 q^{-17} +80 q^{-18} +130 q^{-19} -41 q^{-20} -132 q^{-21} +11 q^{-22} +115 q^{-23} +22 q^{-24} -96 q^{-25} -40 q^{-26} +69 q^{-27} +47 q^{-28} -39 q^{-29} -47 q^{-30} +19 q^{-31} +34 q^{-32} -2 q^{-33} -24 q^{-34} -2 q^{-35} +11 q^{-36} +5 q^{-37} -6 q^{-38} -2 q^{-39} + q^{-40} +2 q^{-41} - q^{-42} </math> \|
	coloured_jones_4 = \|		coloured_jones_4 = <math>\textrm{NotAvailable}(q)</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 =
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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, 68]]</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, 68]]</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[12, 4, 13, 3], X[20, 13, 1, 14], X[16, 5, 17, 6],		<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[12, 4, 13, 3], X[20, 13, 1, 14], X[16, 5, 17, 6],
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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, 68]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_68_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, 68]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_68_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, 68]]&) /@ {~~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, 68]]&) /@ {
			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, 2, 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, 2, 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, 68]][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, 68]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:37, 30 August 2005

2005-08-30T14:37:40Z

Show changes

DrorsRobot at 01:05, 30 August 2005

2005-08-30T01:05:05Z

← Older revision		Revision as of 21:05, 29 August 2005
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	[[Category:Knot Page]]		[[Category:Knot Page]]

DrorsRobot at 22:18, 29 August 2005

2005-08-29T22:18:57Z

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ScottTestRobot at 00:11, 29 August 2005

2005-08-29T00:11:01Z

← Older revision		Revision as of 20:11, 28 August 2005
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ScottTestRobot at 00:01, 29 August 2005

2005-08-29T00:01:21Z

← Older revision		Revision as of 20:01, 28 August 2005
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	{{Category:Knot Page}}		[[Category:Knot Page]]

ScottTestRobot at 23:59, 28 August 2005

2005-08-28T23:59:16Z

← Older revision		Revision as of 19:59, 28 August 2005
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		⚫	{{Rolfsen Knot Page Header\|n=10\|k=68\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,4,-9,8,-5,6,-7,10,-2,3,-8,9,-4,7,-6,5,-3/goTop.html}}
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⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=68\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,4,-9,8,-5,6,-7,10,-2,3,-8,9,-4,7,-6,5,-3/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>.

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	<tr align=center><td>-13</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>-13</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>-15</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>-15</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>
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	2 q t + q t</nowiki></pre></td></tr>		2 q t + q t</nowiki></pre></td></tr>
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ScottTestRobot at 01:47, 28 August 2005

2005-08-28T01:47:43Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:19Z

Resetting knot page to basic template.

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