ScottTestRobot at 22:02, 1 September 2005

2005-09-01T22:02:03Z

DrorsRobot at 22:47, 31 August 2005

2005-08-31T22:47:33Z

← Older revision		Revision as of 18:47, 31 August 2005
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	coloured_jones_5 = <math>-2 q^{132}+2 q^{129}+2 q^{128}+4 q^{127}-q^{126}-3 q^{125}-7 q^{124}-5 q^{123}+2 q^{122}+10 q^{121}+14 q^{120}+10 q^{119}-13 q^{118}-27 q^{117}-23 q^{116}+37 q^{114}+48 q^{113}+11 q^{112}-45 q^{111}-63 q^{110}-33 q^{109}+41 q^{108}+83 q^{107}+51 q^{106}-37 q^{105}-89 q^{104}-64 q^{103}+26 q^{102}+92 q^{101}+74 q^{100}-19 q^{99}-90 q^{98}-76 q^{97}+15 q^{96}+86 q^{95}+75 q^{94}-12 q^{93}-85 q^{92}-71 q^{91}+11 q^{90}+81 q^{89}+71 q^{88}-12 q^{87}-79 q^{86}-65 q^{85}+8 q^{84}+72 q^{83}+66 q^{82}-2 q^{81}-66 q^{80}-63 q^{79}-5 q^{78}+53 q^{77}+63 q^{76}+17 q^{75}-44 q^{74}-59 q^{73}-24 q^{72}+24 q^{71}+53 q^{70}+36 q^{69}-13 q^{68}-42 q^{67}-36 q^{66}-6 q^{65}+27 q^{64}+38 q^{63}+16 q^{62}-13 q^{61}-27 q^{60}-24 q^{59}-3 q^{58}+17 q^{57}+20 q^{56}+14 q^{55}-4 q^{54}-15 q^{53}-14 q^{52}-5 q^{51}+2 q^{50}+12 q^{49}+9 q^{48}+3 q^{47}-3 q^{46}-5 q^{45}-8 q^{44}-3 q^{43}+q^{42}+5 q^{41}+4 q^{40}+5 q^{39}-q^{38}-3 q^{37}-5 q^{36}-4 q^{35}+5 q^{33}+3 q^{32}+3 q^{31}-q^{30}-4 q^{29}-3 q^{28}+2 q^{27}+2 q^{25}+2 q^{24}-q^{23}-2 q^{22}+q^{21}+q^{18}-q^{16}+q^{15}</math> \|		coloured_jones_5 = <math>-2 q^{132}+2 q^{129}+2 q^{128}+4 q^{127}-q^{126}-3 q^{125}-7 q^{124}-5 q^{123}+2 q^{122}+10 q^{121}+14 q^{120}+10 q^{119}-13 q^{118}-27 q^{117}-23 q^{116}+37 q^{114}+48 q^{113}+11 q^{112}-45 q^{111}-63 q^{110}-33 q^{109}+41 q^{108}+83 q^{107}+51 q^{106}-37 q^{105}-89 q^{104}-64 q^{103}+26 q^{102}+92 q^{101}+74 q^{100}-19 q^{99}-90 q^{98}-76 q^{97}+15 q^{96}+86 q^{95}+75 q^{94}-12 q^{93}-85 q^{92}-71 q^{91}+11 q^{90}+81 q^{89}+71 q^{88}-12 q^{87}-79 q^{86}-65 q^{85}+8 q^{84}+72 q^{83}+66 q^{82}-2 q^{81}-66 q^{80}-63 q^{79}-5 q^{78}+53 q^{77}+63 q^{76}+17 q^{75}-44 q^{74}-59 q^{73}-24 q^{72}+24 q^{71}+53 q^{70}+36 q^{69}-13 q^{68}-42 q^{67}-36 q^{66}-6 q^{65}+27 q^{64}+38 q^{63}+16 q^{62}-13 q^{61}-27 q^{60}-24 q^{59}-3 q^{58}+17 q^{57}+20 q^{56}+14 q^{55}-4 q^{54}-15 q^{53}-14 q^{52}-5 q^{51}+2 q^{50}+12 q^{49}+9 q^{48}+3 q^{47}-3 q^{46}-5 q^{45}-8 q^{44}-3 q^{43}+q^{42}+5 q^{41}+4 q^{40}+5 q^{39}-q^{38}-3 q^{37}-5 q^{36}-4 q^{35}+5 q^{33}+3 q^{32}+3 q^{31}-q^{30}-4 q^{29}-3 q^{28}+2 q^{27}+2 q^{25}+2 q^{24}-q^{23}-2 q^{22}+q^{21}+q^{18}-q^{16}+q^{15}</math> \|
	coloured_jones_6 = <math>q^{183}+2 q^{181}-2 q^{179}-4 q^{178}-4 q^{177}-3 q^{176}+q^{175}+10 q^{174}+9 q^{173}+8 q^{172}-q^{171}-7 q^{170}-25 q^{169}-23 q^{168}-q^{167}+14 q^{166}+37 q^{165}+38 q^{164}+33 q^{163}-28 q^{162}-65 q^{161}-63 q^{160}-45 q^{159}+27 q^{158}+88 q^{157}+136 q^{156}+42 q^{155}-58 q^{154}-131 q^{153}-156 q^{152}-60 q^{151}+83 q^{150}+227 q^{149}+151 q^{148}+16 q^{147}-138 q^{146}-234 q^{145}-161 q^{144}+27 q^{143}+247 q^{142}+211 q^{141}+87 q^{140}-101 q^{139}-245 q^{138}-204 q^{137}-20 q^{136}+228 q^{135}+215 q^{134}+111 q^{133}-76 q^{132}-230 q^{131}-205 q^{130}-29 q^{129}+216 q^{128}+203 q^{127}+106 q^{126}-73 q^{125}-220 q^{124}-197 q^{123}-25 q^{122}+211 q^{121}+192 q^{120}+103 q^{119}-68 q^{118}-208 q^{117}-190 q^{116}-33 q^{115}+193 q^{114}+178 q^{113}+110 q^{112}-43 q^{111}-180 q^{110}-182 q^{109}-60 q^{108}+145 q^{107}+154 q^{106}+126 q^{105}+5 q^{104}-129 q^{103}-167 q^{102}-100 q^{101}+70 q^{100}+110 q^{99}+135 q^{98}+65 q^{97}-52 q^{96}-127 q^{95}-126 q^{94}-12 q^{93}+37 q^{92}+110 q^{91}+102 q^{90}+30 q^{89}-50 q^{88}-104 q^{87}-62 q^{86}-41 q^{85}+38 q^{84}+80 q^{83}+69 q^{82}+28 q^{81}-32 q^{80}-43 q^{79}-68 q^{78}-29 q^{77}+12 q^{76}+37 q^{75}+49 q^{74}+23 q^{73}+14 q^{72}-29 q^{71}-33 q^{70}-28 q^{69}-16 q^{68}+14 q^{67}+14 q^{66}+32 q^{65}+13 q^{64}+4 q^{63}-11 q^{62}-22 q^{61}-8 q^{60}-17 q^{59}+7 q^{58}+8 q^{57}+15 q^{56}+8 q^{55}+6 q^{53}-16 q^{52}-4 q^{51}-7 q^{50}+q^{49}-q^{48}+2 q^{47}+14 q^{46}-3 q^{45}+4 q^{44}-3 q^{43}-q^{42}-8 q^{41}-5 q^{40}+7 q^{39}-2 q^{38}+5 q^{37}+2 q^{36}+3 q^{35}-4 q^{34}-4 q^{33}+3 q^{32}-3 q^{31}+q^{30}+q^{29}+3 q^{28}-q^{27}-2 q^{26}+2 q^{25}-q^{24}+q^{21}-q^{19}+q^{18}</math> \|		coloured_jones_6 = <math>q^{183}+2 q^{181}-2 q^{179}-4 q^{178}-4 q^{177}-3 q^{176}+q^{175}+10 q^{174}+9 q^{173}+8 q^{172}-q^{171}-7 q^{170}-25 q^{169}-23 q^{168}-q^{167}+14 q^{166}+37 q^{165}+38 q^{164}+33 q^{163}-28 q^{162}-65 q^{161}-63 q^{160}-45 q^{159}+27 q^{158}+88 q^{157}+136 q^{156}+42 q^{155}-58 q^{154}-131 q^{153}-156 q^{152}-60 q^{151}+83 q^{150}+227 q^{149}+151 q^{148}+16 q^{147}-138 q^{146}-234 q^{145}-161 q^{144}+27 q^{143}+247 q^{142}+211 q^{141}+87 q^{140}-101 q^{139}-245 q^{138}-204 q^{137}-20 q^{136}+228 q^{135}+215 q^{134}+111 q^{133}-76 q^{132}-230 q^{131}-205 q^{130}-29 q^{129}+216 q^{128}+203 q^{127}+106 q^{126}-73 q^{125}-220 q^{124}-197 q^{123}-25 q^{122}+211 q^{121}+192 q^{120}+103 q^{119}-68 q^{118}-208 q^{117}-190 q^{116}-33 q^{115}+193 q^{114}+178 q^{113}+110 q^{112}-43 q^{111}-180 q^{110}-182 q^{109}-60 q^{108}+145 q^{107}+154 q^{106}+126 q^{105}+5 q^{104}-129 q^{103}-167 q^{102}-100 q^{101}+70 q^{100}+110 q^{99}+135 q^{98}+65 q^{97}-52 q^{96}-127 q^{95}-126 q^{94}-12 q^{93}+37 q^{92}+110 q^{91}+102 q^{90}+30 q^{89}-50 q^{88}-104 q^{87}-62 q^{86}-41 q^{85}+38 q^{84}+80 q^{83}+69 q^{82}+28 q^{81}-32 q^{80}-43 q^{79}-68 q^{78}-29 q^{77}+12 q^{76}+37 q^{75}+49 q^{74}+23 q^{73}+14 q^{72}-29 q^{71}-33 q^{70}-28 q^{69}-16 q^{68}+14 q^{67}+14 q^{66}+32 q^{65}+13 q^{64}+4 q^{63}-11 q^{62}-22 q^{61}-8 q^{60}-17 q^{59}+7 q^{58}+8 q^{57}+15 q^{56}+8 q^{55}+6 q^{53}-16 q^{52}-4 q^{51}-7 q^{50}+q^{49}-q^{48}+2 q^{47}+14 q^{46}-3 q^{45}+4 q^{44}-3 q^{43}-q^{42}-8 q^{41}-5 q^{40}+7 q^{39}-2 q^{38}+5 q^{37}+2 q^{36}+3 q^{35}-4 q^{34}-4 q^{33}+3 q^{32}-3 q^{31}+q^{30}+q^{29}+3 q^{28}-q^{27}-2 q^{26}+2 q^{25}-q^{24}+q^{21}-q^{19}+q^{18}</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, 142]]</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, 142]]</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[10, 4, 11, 3], 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[4, 2, 5, 1], X[10, 4, 11, 3], 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, 142]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_142_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, 142]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_142_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, 142]]&) /@ {~~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, 142]]&) /@ {
			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, 3, 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, 3, 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, 142]][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, 142]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:38, 30 August 2005

2005-08-30T14:38:01Z

Show changes

DrorsRobot at 01:05, 30 August 2005

2005-08-30T01:05:23Z

← Older revision		Revision as of 21:05, 29 August 2005
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			{\| 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 22:25, 29 August 2005

2005-08-29T22:25:27Z

Show changes

ScottTestRobot at 00:11, 29 August 2005

2005-08-29T00:11:19Z

← Older revision		Revision as of 20:11, 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=142\|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
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=142\|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>
	<tr align=center>		<tr align=center>
	<td width=16.6667%><table cellpadding=0 cellspacing=0>		<td width=16.6667%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>7</td><td bgcolor=yellow>1</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>		<tr align=center><td>7</td><td bgcolor=yellow>1</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</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>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>1</td></tr>
	</table>~~</center>~~		</table>}}

	{{Computer Talk Header}}		{{Computer Talk Header}}

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	2 q t + 2 q t + 2 q t</nowiki></pre></td></tr>		2 q t + 2 q t + 2 q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:48, 28 August 2005

2005-08-28T01:48:01Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:27Z

Resetting knot page to basic template.

New page

10 142 - Revision history

ScottTestRobot at 22:02, 1 September 2005

DrorsRobot at 22:47, 31 August 2005

ScottKnotPageRobot at 14:38, 30 August 2005

DrorsRobot at 01:05, 30 August 2005

DrorsRobot at 22:25, 29 August 2005

ScottTestRobot at 00:11, 29 August 2005

ScottTestRobot at 01:48, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.