ScottTestRobot at 22:03, 1 September 2005

2005-09-01T22:03:40Z

DrorsRobot at 22:51, 31 August 2005

2005-08-31T22:51:00Z

← Older revision		Revision as of 18:51, 31 August 2005
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	coloured_jones_5 = <math>q^{136}-q^{135}-3 q^{134}+4 q^{132}+5 q^{131}+6 q^{130}-7 q^{129}-22 q^{128}-13 q^{127}+12 q^{126}+40 q^{125}+39 q^{124}-7 q^{123}-70 q^{122}-86 q^{121}-12 q^{120}+105 q^{119}+144 q^{118}+53 q^{117}-117 q^{116}-225 q^{115}-123 q^{114}+133 q^{113}+288 q^{112}+196 q^{111}-99 q^{110}-349 q^{109}-284 q^{108}+74 q^{107}+378 q^{106}+342 q^{105}-17 q^{104}-387 q^{103}-397 q^{102}-17 q^{101}+375 q^{100}+414 q^{99}+60 q^{98}-360 q^{97}-424 q^{96}-76 q^{95}+335 q^{94}+414 q^{93}+94 q^{92}-314 q^{91}-404 q^{90}-100 q^{89}+291 q^{88}+385 q^{87}+112 q^{86}-261 q^{85}-368 q^{84}-130 q^{83}+228 q^{82}+350 q^{81}+145 q^{80}-179 q^{79}-322 q^{78}-176 q^{77}+130 q^{76}+293 q^{75}+186 q^{74}-66 q^{73}-240 q^{72}-210 q^{71}+11 q^{70}+191 q^{69}+192 q^{68}+49 q^{67}-120 q^{66}-180 q^{65}-81 q^{64}+61 q^{63}+128 q^{62}+102 q^{61}+q^{60}-88 q^{59}-87 q^{58}-31 q^{57}+24 q^{56}+67 q^{55}+49 q^{54}+q^{53}-25 q^{52}-31 q^{51}-35 q^{50}-2 q^{49}+18 q^{48}+21 q^{47}+21 q^{46}+15 q^{45}-19 q^{44}-24 q^{43}-19 q^{42}-6 q^{41}+14 q^{40}+28 q^{39}+10 q^{38}-3 q^{37}-16 q^{36}-18 q^{35}-5 q^{34}+13 q^{33}+9 q^{32}+8 q^{31}-q^{30}-9 q^{29}-7 q^{28}+4 q^{27}+q^{26}+3 q^{25}+3 q^{24}-2 q^{23}-3 q^{22}+2 q^{21}+q^{18}-q^{16}+q^{15}</math> \|		coloured_jones_5 = <math>q^{136}-q^{135}-3 q^{134}+4 q^{132}+5 q^{131}+6 q^{130}-7 q^{129}-22 q^{128}-13 q^{127}+12 q^{126}+40 q^{125}+39 q^{124}-7 q^{123}-70 q^{122}-86 q^{121}-12 q^{120}+105 q^{119}+144 q^{118}+53 q^{117}-117 q^{116}-225 q^{115}-123 q^{114}+133 q^{113}+288 q^{112}+196 q^{111}-99 q^{110}-349 q^{109}-284 q^{108}+74 q^{107}+378 q^{106}+342 q^{105}-17 q^{104}-387 q^{103}-397 q^{102}-17 q^{101}+375 q^{100}+414 q^{99}+60 q^{98}-360 q^{97}-424 q^{96}-76 q^{95}+335 q^{94}+414 q^{93}+94 q^{92}-314 q^{91}-404 q^{90}-100 q^{89}+291 q^{88}+385 q^{87}+112 q^{86}-261 q^{85}-368 q^{84}-130 q^{83}+228 q^{82}+350 q^{81}+145 q^{80}-179 q^{79}-322 q^{78}-176 q^{77}+130 q^{76}+293 q^{75}+186 q^{74}-66 q^{73}-240 q^{72}-210 q^{71}+11 q^{70}+191 q^{69}+192 q^{68}+49 q^{67}-120 q^{66}-180 q^{65}-81 q^{64}+61 q^{63}+128 q^{62}+102 q^{61}+q^{60}-88 q^{59}-87 q^{58}-31 q^{57}+24 q^{56}+67 q^{55}+49 q^{54}+q^{53}-25 q^{52}-31 q^{51}-35 q^{50}-2 q^{49}+18 q^{48}+21 q^{47}+21 q^{46}+15 q^{45}-19 q^{44}-24 q^{43}-19 q^{42}-6 q^{41}+14 q^{40}+28 q^{39}+10 q^{38}-3 q^{37}-16 q^{36}-18 q^{35}-5 q^{34}+13 q^{33}+9 q^{32}+8 q^{31}-q^{30}-9 q^{29}-7 q^{28}+4 q^{27}+q^{26}+3 q^{25}+3 q^{24}-2 q^{23}-3 q^{22}+2 q^{21}+q^{18}-q^{16}+q^{15}</math> \|
	coloured_jones_6 = <math>q^{191}-2 q^{190}-q^{189}+2 q^{188}+q^{187}+q^{186}-2 q^{185}+7 q^{184}-5 q^{183}-9 q^{182}-q^{181}-4 q^{180}+q^{179}+5 q^{178}+41 q^{177}+13 q^{176}-15 q^{175}-32 q^{174}-61 q^{173}-58 q^{172}-3 q^{171}+144 q^{170}+138 q^{169}+75 q^{168}-45 q^{167}-211 q^{166}-296 q^{165}-171 q^{164}+224 q^{163}+406 q^{162}+406 q^{161}+146 q^{160}-324 q^{159}-706 q^{158}-618 q^{157}+67 q^{156}+622 q^{155}+896 q^{154}+618 q^{153}-183 q^{152}-1024 q^{151}-1173 q^{150}-351 q^{149}+570 q^{148}+1238 q^{147}+1131 q^{146}+177 q^{145}-1046 q^{144}-1516 q^{143}-763 q^{142}+320 q^{141}+1279 q^{140}+1408 q^{139}+497 q^{138}-881 q^{137}-1568 q^{136}-955 q^{135}+105 q^{134}+1157 q^{133}+1437 q^{132}+630 q^{131}-729 q^{130}-1483 q^{129}-962 q^{128}+11 q^{127}+1032 q^{126}+1365 q^{125}+647 q^{124}-627 q^{123}-1379 q^{122}-923 q^{121}-49 q^{120}+912 q^{119}+1280 q^{118}+670 q^{117}-485 q^{116}-1247 q^{115}-909 q^{114}-176 q^{113}+720 q^{112}+1173 q^{111}+749 q^{110}-234 q^{109}-1029 q^{108}-898 q^{107}-386 q^{106}+411 q^{105}+985 q^{104}+832 q^{103}+108 q^{102}-681 q^{101}-802 q^{100}-595 q^{99}+13 q^{98}+656 q^{97}+798 q^{96}+427 q^{95}-237 q^{94}-533 q^{93}-646 q^{92}-339 q^{91}+213 q^{90}+547 q^{89}+545 q^{88}+147 q^{87}-132 q^{86}-439 q^{85}-452 q^{84}-157 q^{83}+153 q^{82}+377 q^{81}+266 q^{80}+181 q^{79}-94 q^{78}-272 q^{77}-247 q^{76}-128 q^{75}+89 q^{74}+111 q^{73}+214 q^{72}+110 q^{71}-18 q^{70}-96 q^{69}-134 q^{68}-46 q^{67}-70 q^{66}+62 q^{65}+73 q^{64}+65 q^{63}+33 q^{62}-13 q^{61}+8 q^{60}-84 q^{59}-27 q^{58}-23 q^{57}+6 q^{56}+19 q^{55}+28 q^{54}+62 q^{53}-15 q^{52}-2 q^{51}-30 q^{50}-26 q^{49}-27 q^{48}-3 q^{47}+42 q^{46}+7 q^{45}+22 q^{44}-7 q^{42}-25 q^{41}-16 q^{40}+13 q^{39}-2 q^{38}+12 q^{37}+7 q^{36}+5 q^{35}-9 q^{34}-8 q^{33}+5 q^{32}-4 q^{31}+2 q^{30}+2 q^{29}+4 q^{28}-2 q^{27}-3 q^{26}+3 q^{25}-q^{24}+q^{21}-q^{19}+q^{18}</math> \|		coloured_jones_6 = <math>q^{191}-2 q^{190}-q^{189}+2 q^{188}+q^{187}+q^{186}-2 q^{185}+7 q^{184}-5 q^{183}-9 q^{182}-q^{181}-4 q^{180}+q^{179}+5 q^{178}+41 q^{177}+13 q^{176}-15 q^{175}-32 q^{174}-61 q^{173}-58 q^{172}-3 q^{171}+144 q^{170}+138 q^{169}+75 q^{168}-45 q^{167}-211 q^{166}-296 q^{165}-171 q^{164}+224 q^{163}+406 q^{162}+406 q^{161}+146 q^{160}-324 q^{159}-706 q^{158}-618 q^{157}+67 q^{156}+622 q^{155}+896 q^{154}+618 q^{153}-183 q^{152}-1024 q^{151}-1173 q^{150}-351 q^{149}+570 q^{148}+1238 q^{147}+1131 q^{146}+177 q^{145}-1046 q^{144}-1516 q^{143}-763 q^{142}+320 q^{141}+1279 q^{140}+1408 q^{139}+497 q^{138}-881 q^{137}-1568 q^{136}-955 q^{135}+105 q^{134}+1157 q^{133}+1437 q^{132}+630 q^{131}-729 q^{130}-1483 q^{129}-962 q^{128}+11 q^{127}+1032 q^{126}+1365 q^{125}+647 q^{124}-627 q^{123}-1379 q^{122}-923 q^{121}-49 q^{120}+912 q^{119}+1280 q^{118}+670 q^{117}-485 q^{116}-1247 q^{115}-909 q^{114}-176 q^{113}+720 q^{112}+1173 q^{111}+749 q^{110}-234 q^{109}-1029 q^{108}-898 q^{107}-386 q^{106}+411 q^{105}+985 q^{104}+832 q^{103}+108 q^{102}-681 q^{101}-802 q^{100}-595 q^{99}+13 q^{98}+656 q^{97}+798 q^{96}+427 q^{95}-237 q^{94}-533 q^{93}-646 q^{92}-339 q^{91}+213 q^{90}+547 q^{89}+545 q^{88}+147 q^{87}-132 q^{86}-439 q^{85}-452 q^{84}-157 q^{83}+153 q^{82}+377 q^{81}+266 q^{80}+181 q^{79}-94 q^{78}-272 q^{77}-247 q^{76}-128 q^{75}+89 q^{74}+111 q^{73}+214 q^{72}+110 q^{71}-18 q^{70}-96 q^{69}-134 q^{68}-46 q^{67}-70 q^{66}+62 q^{65}+73 q^{64}+65 q^{63}+33 q^{62}-13 q^{61}+8 q^{60}-84 q^{59}-27 q^{58}-23 q^{57}+6 q^{56}+19 q^{55}+28 q^{54}+62 q^{53}-15 q^{52}-2 q^{51}-30 q^{50}-26 q^{49}-27 q^{48}-3 q^{47}+42 q^{46}+7 q^{45}+22 q^{44}-7 q^{42}-25 q^{41}-16 q^{40}+13 q^{39}-2 q^{38}+12 q^{37}+7 q^{36}+5 q^{35}-9 q^{34}-8 q^{33}+5 q^{32}-4 q^{31}+2 q^{30}+2 q^{29}+4 q^{28}-2 q^{27}-3 q^{26}+3 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, 134]]</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, 134]]</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[8, 4, 9, 3], X[9, 15, 10, 14], X[5, 13, 6, 12],		<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[8, 4, 9, 3], X[9, 15, 10, 14], X[5, 13, 6, 12],
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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, 134]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_134_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, 134]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_134_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, 134]]&) /@ {~~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, 134]]&) /@ {
			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, 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, 3, 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, 134]][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, 134]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:39, 30 August 2005

2005-08-30T14:39:39Z

Show changes

DrorsRobot at 01:07, 30 August 2005

2005-08-30T01:07:16Z

← Older revision		Revision as of 21:07, 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 22:24, 29 August 2005

2005-08-29T22:24:40Z

Show changes

ScottTestRobot at 00:13, 29 August 2005

2005-08-29T00:13:27Z

← Older revision		Revision as of 20:13, 28 August 2005
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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=134\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,-4,5,10,-2,-3,9,-6,4,-5,3,-7,8,-9,6,-8,7/goTop.html}}
	{\| align=left
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=134\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,-4,5,10,-2,-3,9,-6,4,-5,3,-7,8,-9,6,-8,7/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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	<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> </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> </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> </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>1</td></tr>
	</table>~~</center>~~		</table>}}

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

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

			[[Category:Knot Page]]

ScottTestRobot at 01:50, 28 August 2005

2005-08-28T01:50:01Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:20Z

Resetting knot page to basic template.

New page

10 134 - Revision history

ScottTestRobot at 22:03, 1 September 2005

DrorsRobot at 22:51, 31 August 2005

ScottKnotPageRobot at 14:39, 30 August 2005

DrorsRobot at 01:07, 30 August 2005

DrorsRobot at 22:24, 29 August 2005

ScottTestRobot at 00:13, 29 August 2005

ScottTestRobot at 01:50, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.