ScottTestRobot at 22:05, 1 September 2005

2005-09-01T22:05:47Z

DrorsRobot at 22:54, 31 August 2005

2005-08-31T22:54:36Z

← Older revision		Revision as of 18:54, 31 August 2005
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	coloured_jones_4 = <math> q^{-8} -3 q^{-9} +3 q^{-10} +4 q^{-11} -8 q^{-12} +2 q^{-13} -10 q^{-14} +21 q^{-15} +25 q^{-16} -44 q^{-17} -17 q^{-18} -45 q^{-19} +95 q^{-20} +138 q^{-21} -108 q^{-22} -139 q^{-23} -231 q^{-24} +236 q^{-25} +503 q^{-26} -38 q^{-27} -377 q^{-28} -809 q^{-29} +219 q^{-30} +1158 q^{-31} +466 q^{-32} -473 q^{-33} -1785 q^{-34} -269 q^{-35} +1751 q^{-36} +1385 q^{-37} -107 q^{-38} -2731 q^{-39} -1158 q^{-40} +1900 q^{-41} +2279 q^{-42} +627 q^{-43} -3221 q^{-44} -2008 q^{-45} +1606 q^{-46} +2768 q^{-47} +1373 q^{-48} -3202 q^{-49} -2515 q^{-50} +1093 q^{-51} +2809 q^{-52} +1921 q^{-53} -2790 q^{-54} -2672 q^{-55} +459 q^{-56} +2498 q^{-57} +2274 q^{-58} -2054 q^{-59} -2528 q^{-60} -252 q^{-61} +1859 q^{-62} +2382 q^{-63} -1071 q^{-64} -2026 q^{-65} -862 q^{-66} +956 q^{-67} +2086 q^{-68} -131 q^{-69} -1198 q^{-70} -1052 q^{-71} +96 q^{-72} +1364 q^{-73} +365 q^{-74} -364 q^{-75} -743 q^{-76} -328 q^{-77} +572 q^{-78} +330 q^{-79} +77 q^{-80} -284 q^{-81} -281 q^{-82} +118 q^{-83} +111 q^{-84} +112 q^{-85} -40 q^{-86} -102 q^{-87} +7 q^{-88} +5 q^{-89} +35 q^{-90} +4 q^{-91} -19 q^{-92} +2 q^{-93} -3 q^{-94} +5 q^{-95} + q^{-96} -3 q^{-97} + q^{-98} </math> \|		coloured_jones_4 = <math> q^{-8} -3 q^{-9} +3 q^{-10} +4 q^{-11} -8 q^{-12} +2 q^{-13} -10 q^{-14} +21 q^{-15} +25 q^{-16} -44 q^{-17} -17 q^{-18} -45 q^{-19} +95 q^{-20} +138 q^{-21} -108 q^{-22} -139 q^{-23} -231 q^{-24} +236 q^{-25} +503 q^{-26} -38 q^{-27} -377 q^{-28} -809 q^{-29} +219 q^{-30} +1158 q^{-31} +466 q^{-32} -473 q^{-33} -1785 q^{-34} -269 q^{-35} +1751 q^{-36} +1385 q^{-37} -107 q^{-38} -2731 q^{-39} -1158 q^{-40} +1900 q^{-41} +2279 q^{-42} +627 q^{-43} -3221 q^{-44} -2008 q^{-45} +1606 q^{-46} +2768 q^{-47} +1373 q^{-48} -3202 q^{-49} -2515 q^{-50} +1093 q^{-51} +2809 q^{-52} +1921 q^{-53} -2790 q^{-54} -2672 q^{-55} +459 q^{-56} +2498 q^{-57} +2274 q^{-58} -2054 q^{-59} -2528 q^{-60} -252 q^{-61} +1859 q^{-62} +2382 q^{-63} -1071 q^{-64} -2026 q^{-65} -862 q^{-66} +956 q^{-67} +2086 q^{-68} -131 q^{-69} -1198 q^{-70} -1052 q^{-71} +96 q^{-72} +1364 q^{-73} +365 q^{-74} -364 q^{-75} -743 q^{-76} -328 q^{-77} +572 q^{-78} +330 q^{-79} +77 q^{-80} -284 q^{-81} -281 q^{-82} +118 q^{-83} +111 q^{-84} +112 q^{-85} -40 q^{-86} -102 q^{-87} +7 q^{-88} +5 q^{-89} +35 q^{-90} +4 q^{-91} -19 q^{-92} +2 q^{-93} -3 q^{-94} +5 q^{-95} + q^{-96} -3 q^{-97} + q^{-98} </math> \|
	coloured_jones_5 = <math> q^{-10} -3 q^{-11} +3 q^{-12} +4 q^{-13} -8 q^{-14} -2 q^{-15} +6 q^{-16} +12 q^{-18} +7 q^{-19} -33 q^{-20} -37 q^{-21} +22 q^{-22} +55 q^{-23} +82 q^{-24} +11 q^{-25} -145 q^{-26} -224 q^{-27} -54 q^{-28} +267 q^{-29} +477 q^{-30} +270 q^{-31} -394 q^{-32} -953 q^{-33} -729 q^{-34} +373 q^{-35} +1631 q^{-36} +1658 q^{-37} -80 q^{-38} -2379 q^{-39} -3040 q^{-40} -904 q^{-41} +2975 q^{-42} +5037 q^{-43} +2512 q^{-44} -3103 q^{-45} -7067 q^{-46} -5137 q^{-47} +2424 q^{-48} +9222 q^{-49} +8197 q^{-50} -908 q^{-51} -10595 q^{-52} -11714 q^{-53} -1536 q^{-54} +11480 q^{-55} +14870 q^{-56} +4438 q^{-57} -11246 q^{-58} -17656 q^{-59} -7573 q^{-60} +10499 q^{-61} +19516 q^{-62} +10432 q^{-63} -9024 q^{-64} -20712 q^{-65} -12892 q^{-66} +7498 q^{-67} +21044 q^{-68} +14737 q^{-69} -5739 q^{-70} -20919 q^{-71} -16091 q^{-72} +4156 q^{-73} +20295 q^{-74} +16953 q^{-75} -2520 q^{-76} -19340 q^{-77} -17535 q^{-78} +891 q^{-79} +18076 q^{-80} +17809 q^{-81} +828 q^{-82} -16377 q^{-83} -17823 q^{-84} -2746 q^{-85} +14306 q^{-86} +17498 q^{-87} +4643 q^{-88} -11685 q^{-89} -16664 q^{-90} -6553 q^{-91} +8704 q^{-92} +15262 q^{-93} +8050 q^{-94} -5441 q^{-95} -13152 q^{-96} -9040 q^{-97} +2285 q^{-98} +10483 q^{-99} +9150 q^{-100} +522 q^{-101} -7483 q^{-102} -8445 q^{-103} -2518 q^{-104} +4510 q^{-105} +6930 q^{-106} +3639 q^{-107} -1944 q^{-108} -5079 q^{-109} -3758 q^{-110} +121 q^{-111} +3113 q^{-112} +3212 q^{-113} +928 q^{-114} -1549 q^{-115} -2289 q^{-116} -1208 q^{-117} +451 q^{-118} +1356 q^{-119} +1054 q^{-120} +100 q^{-121} -642 q^{-122} -707 q^{-123} -263 q^{-124} +221 q^{-125} +370 q^{-126} +219 q^{-127} -14 q^{-128} -163 q^{-129} -136 q^{-130} -18 q^{-131} +54 q^{-132} +46 q^{-133} +29 q^{-134} -8 q^{-135} -30 q^{-136} -6 q^{-137} +7 q^{-138} + q^{-139} +3 q^{-140} +3 q^{-141} -5 q^{-142} - q^{-143} +3 q^{-144} - q^{-145} </math> \|		coloured_jones_5 = <math> q^{-10} -3 q^{-11} +3 q^{-12} +4 q^{-13} -8 q^{-14} -2 q^{-15} +6 q^{-16} +12 q^{-18} +7 q^{-19} -33 q^{-20} -37 q^{-21} +22 q^{-22} +55 q^{-23} +82 q^{-24} +11 q^{-25} -145 q^{-26} -224 q^{-27} -54 q^{-28} +267 q^{-29} +477 q^{-30} +270 q^{-31} -394 q^{-32} -953 q^{-33} -729 q^{-34} +373 q^{-35} +1631 q^{-36} +1658 q^{-37} -80 q^{-38} -2379 q^{-39} -3040 q^{-40} -904 q^{-41} +2975 q^{-42} +5037 q^{-43} +2512 q^{-44} -3103 q^{-45} -7067 q^{-46} -5137 q^{-47} +2424 q^{-48} +9222 q^{-49} +8197 q^{-50} -908 q^{-51} -10595 q^{-52} -11714 q^{-53} -1536 q^{-54} +11480 q^{-55} +14870 q^{-56} +4438 q^{-57} -11246 q^{-58} -17656 q^{-59} -7573 q^{-60} +10499 q^{-61} +19516 q^{-62} +10432 q^{-63} -9024 q^{-64} -20712 q^{-65} -12892 q^{-66} +7498 q^{-67} +21044 q^{-68} +14737 q^{-69} -5739 q^{-70} -20919 q^{-71} -16091 q^{-72} +4156 q^{-73} +20295 q^{-74} +16953 q^{-75} -2520 q^{-76} -19340 q^{-77} -17535 q^{-78} +891 q^{-79} +18076 q^{-80} +17809 q^{-81} +828 q^{-82} -16377 q^{-83} -17823 q^{-84} -2746 q^{-85} +14306 q^{-86} +17498 q^{-87} +4643 q^{-88} -11685 q^{-89} -16664 q^{-90} -6553 q^{-91} +8704 q^{-92} +15262 q^{-93} +8050 q^{-94} -5441 q^{-95} -13152 q^{-96} -9040 q^{-97} +2285 q^{-98} +10483 q^{-99} +9150 q^{-100} +522 q^{-101} -7483 q^{-102} -8445 q^{-103} -2518 q^{-104} +4510 q^{-105} +6930 q^{-106} +3639 q^{-107} -1944 q^{-108} -5079 q^{-109} -3758 q^{-110} +121 q^{-111} +3113 q^{-112} +3212 q^{-113} +928 q^{-114} -1549 q^{-115} -2289 q^{-116} -1208 q^{-117} +451 q^{-118} +1356 q^{-119} +1054 q^{-120} +100 q^{-121} -642 q^{-122} -707 q^{-123} -263 q^{-124} +221 q^{-125} +370 q^{-126} +219 q^{-127} -14 q^{-128} -163 q^{-129} -136 q^{-130} -18 q^{-131} +54 q^{-132} +46 q^{-133} +29 q^{-134} -8 q^{-135} -30 q^{-136} -6 q^{-137} +7 q^{-138} + q^{-139} +3 q^{-140} +3 q^{-141} -5 q^{-142} - q^{-143} +3 q^{-144} - q^{-145} </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[9, 38]]</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[9, 38]]</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, 6, 2, 7], X[5, 14, 6, 15], X[7, 18, 8, 1], X[15, 8, 16, 9],		<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, 6, 2, 7], X[5, 14, 6, 15], X[7, 18, 8, 1], X[15, 8, 16, 9],
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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[9, 38]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_38_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[9, 38]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_38_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[9, 38]]&) /@ {~~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[9, 38]]&) /@ {
			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}, 2, 3, {4, 7}, 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}, 2, 3, {4, 7}, 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[9, 38]][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[9, 38]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:41, 30 August 2005

2005-08-30T14:41:48Z

Show changes

DrorsRobot at 01:09, 30 August 2005

2005-08-30T01:09:51Z

← Older revision		Revision as of 21:09, 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 22:12, 29 August 2005

2005-08-29T22:12:07Z

Show changes

ScottTestRobot at 00:16, 29 August 2005

2005-08-29T00:16:21Z

← Older revision		Revision as of 20:16, 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=9\|k=38\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,9,-5,6,-2,1,-3,4,-6,5,-8,7,-9,2,-4,8,-7,3/goTop.html}}
	{\| align=left
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=9\|k=38\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,9,-5,6,-2,1,-3,4,-6,5,-8,7,-9,2,-4,8,-7,3/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>
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	<tr align=center><td>-21</td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr>		<tr align=center><td>-21</td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr>
	<tr align=center><td>-23</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>-23</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>
	</table>~~</center>~~		</table>}}

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

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

			[[Category:Knot Page]]

ScottTestRobot at 01:52, 28 August 2005

2005-08-28T01:52:36Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T21:22:31Z

Resetting knot page to basic template.

New page

9 38 - Revision history

ScottTestRobot at 22:05, 1 September 2005

DrorsRobot at 22:54, 31 August 2005

ScottKnotPageRobot at 14:41, 30 August 2005

DrorsRobot at 01:09, 30 August 2005

DrorsRobot at 22:12, 29 August 2005

ScottTestRobot at 00:16, 29 August 2005

ScottTestRobot at 01:52, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.