ScottTestRobot at 22:06, 1 September 2005

2005-09-01T22:06:00Z

DrorsRobot at 22:54, 31 August 2005

2005-08-31T22:54:54Z

← Older revision		Revision as of 18:54, 31 August 2005
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	coloured_jones_5 = <math>q^{32}-4 q^{29}+2 q^{27}+3 q^{26}+2 q^{25}-2 q^{24}-8 q^{23}+q^{22}+11 q^{21}+5 q^{20}-3 q^{19}-17 q^{18}-22 q^{17}+7 q^{16}+43 q^{15}+40 q^{14}-6 q^{13}-64 q^{12}-81 q^{11}-14 q^{10}+97 q^9+131 q^8+42 q^7-113 q^6-186 q^5-86 q^4+115 q^3+234 q^2+137 q-104-267 q^{-1} -178 q^{-2} +82 q^{-3} +275 q^{-4} +214 q^{-5} -55 q^{-6} -279 q^{-7} -228 q^{-8} +37 q^{-9} +266 q^{-10} +234 q^{-11} -21 q^{-12} -258 q^{-13} -227 q^{-14} +15 q^{-15} +241 q^{-16} +226 q^{-17} -12 q^{-18} -232 q^{-19} -214 q^{-20} +2 q^{-21} +212 q^{-22} +214 q^{-23} +11 q^{-24} -196 q^{-25} -208 q^{-26} -29 q^{-27} +165 q^{-28} +205 q^{-29} +56 q^{-30} -138 q^{-31} -195 q^{-32} -74 q^{-33} +96 q^{-34} +176 q^{-35} +101 q^{-36} -58 q^{-37} -154 q^{-38} -104 q^{-39} +16 q^{-40} +112 q^{-41} +111 q^{-42} +19 q^{-43} -78 q^{-44} -92 q^{-45} -39 q^{-46} +31 q^{-47} +68 q^{-48} +46 q^{-49} -2 q^{-50} -36 q^{-51} -36 q^{-52} -14 q^{-53} +6 q^{-54} +17 q^{-55} +16 q^{-56} +9 q^{-57} +6 q^{-58} -4 q^{-59} -13 q^{-60} -17 q^{-61} -11 q^{-62} +2 q^{-63} +21 q^{-64} +21 q^{-65} +6 q^{-66} -9 q^{-67} -21 q^{-68} -19 q^{-69} - q^{-70} +17 q^{-71} +17 q^{-72} +8 q^{-73} -3 q^{-74} -15 q^{-75} -12 q^{-76} +8 q^{-78} +7 q^{-79} +4 q^{-80} -7 q^{-82} -4 q^{-83} + q^{-84} +2 q^{-85} + q^{-86} +2 q^{-87} - q^{-88} -2 q^{-89} + q^{-90} </math> \|		coloured_jones_5 = <math>q^{32}-4 q^{29}+2 q^{27}+3 q^{26}+2 q^{25}-2 q^{24}-8 q^{23}+q^{22}+11 q^{21}+5 q^{20}-3 q^{19}-17 q^{18}-22 q^{17}+7 q^{16}+43 q^{15}+40 q^{14}-6 q^{13}-64 q^{12}-81 q^{11}-14 q^{10}+97 q^9+131 q^8+42 q^7-113 q^6-186 q^5-86 q^4+115 q^3+234 q^2+137 q-104-267 q^{-1} -178 q^{-2} +82 q^{-3} +275 q^{-4} +214 q^{-5} -55 q^{-6} -279 q^{-7} -228 q^{-8} +37 q^{-9} +266 q^{-10} +234 q^{-11} -21 q^{-12} -258 q^{-13} -227 q^{-14} +15 q^{-15} +241 q^{-16} +226 q^{-17} -12 q^{-18} -232 q^{-19} -214 q^{-20} +2 q^{-21} +212 q^{-22} +214 q^{-23} +11 q^{-24} -196 q^{-25} -208 q^{-26} -29 q^{-27} +165 q^{-28} +205 q^{-29} +56 q^{-30} -138 q^{-31} -195 q^{-32} -74 q^{-33} +96 q^{-34} +176 q^{-35} +101 q^{-36} -58 q^{-37} -154 q^{-38} -104 q^{-39} +16 q^{-40} +112 q^{-41} +111 q^{-42} +19 q^{-43} -78 q^{-44} -92 q^{-45} -39 q^{-46} +31 q^{-47} +68 q^{-48} +46 q^{-49} -2 q^{-50} -36 q^{-51} -36 q^{-52} -14 q^{-53} +6 q^{-54} +17 q^{-55} +16 q^{-56} +9 q^{-57} +6 q^{-58} -4 q^{-59} -13 q^{-60} -17 q^{-61} -11 q^{-62} +2 q^{-63} +21 q^{-64} +21 q^{-65} +6 q^{-66} -9 q^{-67} -21 q^{-68} -19 q^{-69} - q^{-70} +17 q^{-71} +17 q^{-72} +8 q^{-73} -3 q^{-74} -15 q^{-75} -12 q^{-76} +8 q^{-78} +7 q^{-79} +4 q^{-80} -7 q^{-82} -4 q^{-83} + q^{-84} +2 q^{-85} + q^{-86} +2 q^{-87} - q^{-88} -2 q^{-89} + q^{-90} </math> \|
	coloured_jones_6 = <math>q^{45}+q^{44}-2 q^{43}-q^{42}-4 q^{41}+q^{40}+2 q^{39}+4 q^{38}+9 q^{37}-3 q^{36}-2 q^{35}-14 q^{34}-3 q^{33}-6 q^{32}+q^{31}+23 q^{30}+10 q^{29}+17 q^{28}-9 q^{27}-q^{26}-41 q^{25}-49 q^{24}-5 q^{23}+11 q^{22}+71 q^{21}+77 q^{20}+92 q^{19}-45 q^{18}-151 q^{17}-159 q^{16}-122 q^{15}+67 q^{14}+228 q^{13}+352 q^{12}+120 q^{11}-177 q^{10}-377 q^9-426 q^8-127 q^7+281 q^6+646 q^5+435 q^4-13 q^3-467 q^2-711 q-430+151 q^{-1} +768 q^{-2} +683 q^{-3} +224 q^{-4} -379 q^{-5} -805 q^{-6} -632 q^{-7} -25 q^{-8} +719 q^{-9} +748 q^{-10} +357 q^{-11} -260 q^{-12} -760 q^{-13} -673 q^{-14} -109 q^{-15} +645 q^{-16} +709 q^{-17} +372 q^{-18} -207 q^{-19} -700 q^{-20} -643 q^{-21} -123 q^{-22} +598 q^{-23} +662 q^{-24} +360 q^{-25} -173 q^{-26} -648 q^{-27} -617 q^{-28} -154 q^{-29} +528 q^{-30} +617 q^{-31} +383 q^{-32} -90 q^{-33} -561 q^{-34} -597 q^{-35} -243 q^{-36} +387 q^{-37} +547 q^{-38} +435 q^{-39} +60 q^{-40} -410 q^{-41} -556 q^{-42} -366 q^{-43} +171 q^{-44} +417 q^{-45} +467 q^{-46} +242 q^{-47} -186 q^{-48} -444 q^{-49} -456 q^{-50} -74 q^{-51} +202 q^{-52} +404 q^{-53} +371 q^{-54} +65 q^{-55} -226 q^{-56} -415 q^{-57} -247 q^{-58} -49 q^{-59} +208 q^{-60} +345 q^{-61} +226 q^{-62} +27 q^{-63} -221 q^{-64} -236 q^{-65} -195 q^{-66} -20 q^{-67} +162 q^{-68} +194 q^{-69} +159 q^{-70} -15 q^{-71} -76 q^{-72} -145 q^{-73} -110 q^{-74} -13 q^{-75} +42 q^{-76} +106 q^{-77} +38 q^{-78} +43 q^{-79} -12 q^{-80} -39 q^{-81} -36 q^{-82} -38 q^{-83} +12 q^{-84} -32 q^{-85} +24 q^{-86} +27 q^{-87} +29 q^{-88} +21 q^{-89} -2 q^{-90} +13 q^{-91} -61 q^{-92} -26 q^{-93} -15 q^{-94} +9 q^{-95} +21 q^{-96} +27 q^{-97} +49 q^{-98} -20 q^{-99} -15 q^{-100} -28 q^{-101} -17 q^{-102} -13 q^{-103} +5 q^{-104} +40 q^{-105} +4 q^{-106} +9 q^{-107} -6 q^{-108} -8 q^{-109} -17 q^{-110} -10 q^{-111} +13 q^{-112} + q^{-113} +8 q^{-114} +3 q^{-115} +3 q^{-116} -7 q^{-117} -6 q^{-118} +3 q^{-119} -2 q^{-120} +2 q^{-121} + q^{-122} +2 q^{-123} - q^{-124} -2 q^{-125} + q^{-126} </math> \|		coloured_jones_6 = <math>q^{45}+q^{44}-2 q^{43}-q^{42}-4 q^{41}+q^{40}+2 q^{39}+4 q^{38}+9 q^{37}-3 q^{36}-2 q^{35}-14 q^{34}-3 q^{33}-6 q^{32}+q^{31}+23 q^{30}+10 q^{29}+17 q^{28}-9 q^{27}-q^{26}-41 q^{25}-49 q^{24}-5 q^{23}+11 q^{22}+71 q^{21}+77 q^{20}+92 q^{19}-45 q^{18}-151 q^{17}-159 q^{16}-122 q^{15}+67 q^{14}+228 q^{13}+352 q^{12}+120 q^{11}-177 q^{10}-377 q^9-426 q^8-127 q^7+281 q^6+646 q^5+435 q^4-13 q^3-467 q^2-711 q-430+151 q^{-1} +768 q^{-2} +683 q^{-3} +224 q^{-4} -379 q^{-5} -805 q^{-6} -632 q^{-7} -25 q^{-8} +719 q^{-9} +748 q^{-10} +357 q^{-11} -260 q^{-12} -760 q^{-13} -673 q^{-14} -109 q^{-15} +645 q^{-16} +709 q^{-17} +372 q^{-18} -207 q^{-19} -700 q^{-20} -643 q^{-21} -123 q^{-22} +598 q^{-23} +662 q^{-24} +360 q^{-25} -173 q^{-26} -648 q^{-27} -617 q^{-28} -154 q^{-29} +528 q^{-30} +617 q^{-31} +383 q^{-32} -90 q^{-33} -561 q^{-34} -597 q^{-35} -243 q^{-36} +387 q^{-37} +547 q^{-38} +435 q^{-39} +60 q^{-40} -410 q^{-41} -556 q^{-42} -366 q^{-43} +171 q^{-44} +417 q^{-45} +467 q^{-46} +242 q^{-47} -186 q^{-48} -444 q^{-49} -456 q^{-50} -74 q^{-51} +202 q^{-52} +404 q^{-53} +371 q^{-54} +65 q^{-55} -226 q^{-56} -415 q^{-57} -247 q^{-58} -49 q^{-59} +208 q^{-60} +345 q^{-61} +226 q^{-62} +27 q^{-63} -221 q^{-64} -236 q^{-65} -195 q^{-66} -20 q^{-67} +162 q^{-68} +194 q^{-69} +159 q^{-70} -15 q^{-71} -76 q^{-72} -145 q^{-73} -110 q^{-74} -13 q^{-75} +42 q^{-76} +106 q^{-77} +38 q^{-78} +43 q^{-79} -12 q^{-80} -39 q^{-81} -36 q^{-82} -38 q^{-83} +12 q^{-84} -32 q^{-85} +24 q^{-86} +27 q^{-87} +29 q^{-88} +21 q^{-89} -2 q^{-90} +13 q^{-91} -61 q^{-92} -26 q^{-93} -15 q^{-94} +9 q^{-95} +21 q^{-96} +27 q^{-97} +49 q^{-98} -20 q^{-99} -15 q^{-100} -28 q^{-101} -17 q^{-102} -13 q^{-103} +5 q^{-104} +40 q^{-105} +4 q^{-106} +9 q^{-107} -6 q^{-108} -8 q^{-109} -17 q^{-110} -10 q^{-111} +13 q^{-112} + q^{-113} +8 q^{-114} +3 q^{-115} +3 q^{-116} -7 q^{-117} -6 q^{-118} +3 q^{-119} -2 q^{-120} +2 q^{-121} + q^{-122} +2 q^{-123} - q^{-124} -2 q^{-125} + q^{-126} </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, 141]]</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, 141]]</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[3, 10, 4, 11], X[14, 6, 15, 5], X[16, 8, 17, 7],		<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[3, 10, 4, 11], X[14, 6, 15, 5], X[16, 8, 17, 7],
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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>3</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>3</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, 141]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_141_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, 141]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_141_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, 141]]&) /@ {~~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, 141]]&) /@ {
			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, 1, 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, 1, 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, 141]][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, 141]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:42, 30 August 2005

2005-08-30T14:42:00Z

Show changes

DrorsRobot at 01:10, 30 August 2005

2005-08-30T01:10:08Z

← Older revision		Revision as of 21:10, 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

2005-08-29T22:25:21Z

Show changes

ScottTestRobot at 00:16, 29 August 2005

2005-08-29T00:16:38Z

← Older revision		Revision as of 20:16, 28 August 2005
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	<span id="top"></span>		<span id="top"></span>
			<!-- -->

	<!-- 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=141\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,3,-5,4,-9,-10,2,-7,8,9,-3,5,-4,-6,7,-8,6/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=141\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,3,-5,4,-9,-10,2,-7,8,9,-3,5,-4,-6,7,-8,6/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=15.3846%><table cellpadding=0 cellspacing=0>		<td width=15.3846%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>-11</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>-1</td></tr>		<tr align=center><td>-11</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>-1</td></tr>
	<tr align=center><td>-13</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>-13</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 q t q t</nowiki></pre></td></tr>		q t q t q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:52, 28 August 2005

2005-08-28T01:52:51Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:26Z

Resetting knot page to basic template.

New page

10 141 - Revision history

ScottTestRobot at 22:06, 1 September 2005

DrorsRobot at 22:54, 31 August 2005

ScottKnotPageRobot at 14:42, 30 August 2005

DrorsRobot at 01:10, 30 August 2005

DrorsRobot at 22:25, 29 August 2005

ScottTestRobot at 00:16, 29 August 2005

ScottTestRobot at 01:52, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.