ScottTestRobot at 22:05, 1 September 2005

2005-09-01T22:05:44Z

DrorsRobot at 22:54, 31 August 2005

2005-08-31T22:54:30Z

← Older revision		Revision as of 18:54, 31 August 2005
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	coloured_jones_5 = <math> q^{-15} - q^{-16} + q^{-18} +2 q^{-21} -3 q^{-22} -2 q^{-23} +3 q^{-24} +3 q^{-25} +5 q^{-27} -7 q^{-28} -10 q^{-29} - q^{-30} +7 q^{-31} +8 q^{-32} +18 q^{-33} -4 q^{-34} -23 q^{-35} -20 q^{-36} -7 q^{-37} +12 q^{-38} +46 q^{-39} +25 q^{-40} -15 q^{-41} -40 q^{-42} -49 q^{-43} -22 q^{-44} +55 q^{-45} +70 q^{-46} +33 q^{-47} -17 q^{-48} -79 q^{-49} -89 q^{-50} +4 q^{-51} +77 q^{-52} +90 q^{-53} +56 q^{-54} -45 q^{-55} -125 q^{-56} -80 q^{-57} +10 q^{-58} +92 q^{-59} +126 q^{-60} +47 q^{-61} -80 q^{-62} -128 q^{-63} -95 q^{-64} +15 q^{-65} +139 q^{-66} +143 q^{-67} +26 q^{-68} -104 q^{-69} -178 q^{-70} -103 q^{-71} +87 q^{-72} +201 q^{-73} +146 q^{-74} -29 q^{-75} -218 q^{-76} -215 q^{-77} +3 q^{-78} +225 q^{-79} +253 q^{-80} +47 q^{-81} -231 q^{-82} -308 q^{-83} -74 q^{-84} +240 q^{-85} +340 q^{-86} +115 q^{-87} -246 q^{-88} -388 q^{-89} -139 q^{-90} +251 q^{-91} +416 q^{-92} +181 q^{-93} -248 q^{-94} -453 q^{-95} -207 q^{-96} +233 q^{-97} +458 q^{-98} +249 q^{-99} -200 q^{-100} -458 q^{-101} -275 q^{-102} +158 q^{-103} +424 q^{-104} +288 q^{-105} -98 q^{-106} -372 q^{-107} -288 q^{-108} +48 q^{-109} +305 q^{-110} +254 q^{-111} -3 q^{-112} -218 q^{-113} -221 q^{-114} -29 q^{-115} +160 q^{-116} +157 q^{-117} +37 q^{-118} -83 q^{-119} -118 q^{-120} -40 q^{-121} +53 q^{-122} +65 q^{-123} +29 q^{-124} -15 q^{-125} -40 q^{-126} -20 q^{-127} +8 q^{-128} +11 q^{-129} +13 q^{-130} +6 q^{-131} -9 q^{-132} -5 q^{-133} -5 q^{-135} + q^{-136} +10 q^{-137} -4 q^{-138} - q^{-139} +3 q^{-140} -5 q^{-141} - q^{-142} +5 q^{-143} -2 q^{-144} - q^{-145} +2 q^{-146} - q^{-147} - q^{-148} +2 q^{-149} - q^{-150} </math> \|		coloured_jones_5 = <math> q^{-15} - q^{-16} + q^{-18} +2 q^{-21} -3 q^{-22} -2 q^{-23} +3 q^{-24} +3 q^{-25} +5 q^{-27} -7 q^{-28} -10 q^{-29} - q^{-30} +7 q^{-31} +8 q^{-32} +18 q^{-33} -4 q^{-34} -23 q^{-35} -20 q^{-36} -7 q^{-37} +12 q^{-38} +46 q^{-39} +25 q^{-40} -15 q^{-41} -40 q^{-42} -49 q^{-43} -22 q^{-44} +55 q^{-45} +70 q^{-46} +33 q^{-47} -17 q^{-48} -79 q^{-49} -89 q^{-50} +4 q^{-51} +77 q^{-52} +90 q^{-53} +56 q^{-54} -45 q^{-55} -125 q^{-56} -80 q^{-57} +10 q^{-58} +92 q^{-59} +126 q^{-60} +47 q^{-61} -80 q^{-62} -128 q^{-63} -95 q^{-64} +15 q^{-65} +139 q^{-66} +143 q^{-67} +26 q^{-68} -104 q^{-69} -178 q^{-70} -103 q^{-71} +87 q^{-72} +201 q^{-73} +146 q^{-74} -29 q^{-75} -218 q^{-76} -215 q^{-77} +3 q^{-78} +225 q^{-79} +253 q^{-80} +47 q^{-81} -231 q^{-82} -308 q^{-83} -74 q^{-84} +240 q^{-85} +340 q^{-86} +115 q^{-87} -246 q^{-88} -388 q^{-89} -139 q^{-90} +251 q^{-91} +416 q^{-92} +181 q^{-93} -248 q^{-94} -453 q^{-95} -207 q^{-96} +233 q^{-97} +458 q^{-98} +249 q^{-99} -200 q^{-100} -458 q^{-101} -275 q^{-102} +158 q^{-103} +424 q^{-104} +288 q^{-105} -98 q^{-106} -372 q^{-107} -288 q^{-108} +48 q^{-109} +305 q^{-110} +254 q^{-111} -3 q^{-112} -218 q^{-113} -221 q^{-114} -29 q^{-115} +160 q^{-116} +157 q^{-117} +37 q^{-118} -83 q^{-119} -118 q^{-120} -40 q^{-121} +53 q^{-122} +65 q^{-123} +29 q^{-124} -15 q^{-125} -40 q^{-126} -20 q^{-127} +8 q^{-128} +11 q^{-129} +13 q^{-130} +6 q^{-131} -9 q^{-132} -5 q^{-133} -5 q^{-135} + q^{-136} +10 q^{-137} -4 q^{-138} - q^{-139} +3 q^{-140} -5 q^{-141} - q^{-142} +5 q^{-143} -2 q^{-144} - q^{-145} +2 q^{-146} - q^{-147} - q^{-148} +2 q^{-149} - q^{-150} </math> \|
	coloured_jones_6 = <math> q^{-18} - q^{-19} + q^{-21} - q^{-24} +3 q^{-25} -3 q^{-26} -2 q^{-27} +4 q^{-28} +2 q^{-29} +2 q^{-30} -5 q^{-31} +6 q^{-32} -8 q^{-33} -10 q^{-34} +5 q^{-35} +7 q^{-36} +12 q^{-37} -4 q^{-38} +18 q^{-39} -15 q^{-40} -31 q^{-41} -11 q^{-42} +24 q^{-44} +8 q^{-45} +61 q^{-46} +4 q^{-47} -42 q^{-48} -48 q^{-49} -45 q^{-50} -7 q^{-51} -9 q^{-52} +124 q^{-53} +70 q^{-54} +16 q^{-55} -43 q^{-56} -89 q^{-57} -93 q^{-58} -120 q^{-59} +117 q^{-60} +113 q^{-61} +129 q^{-62} +64 q^{-63} -18 q^{-64} -129 q^{-65} -276 q^{-66} -5 q^{-67} +14 q^{-68} +156 q^{-69} +182 q^{-70} +185 q^{-71} +5 q^{-72} -308 q^{-73} -113 q^{-74} -206 q^{-75} -13 q^{-76} +126 q^{-77} +355 q^{-78} +253 q^{-79} -124 q^{-80} -26 q^{-81} -357 q^{-82} -291 q^{-83} -164 q^{-84} +313 q^{-85} +420 q^{-86} +167 q^{-87} +284 q^{-88} -282 q^{-89} -481 q^{-90} -558 q^{-91} +50 q^{-92} +373 q^{-93} +381 q^{-94} +683 q^{-95} +5 q^{-96} -478 q^{-97} -885 q^{-98} -304 q^{-99} +139 q^{-100} +440 q^{-101} +1024 q^{-102} +374 q^{-103} -325 q^{-104} -1077 q^{-105} -618 q^{-106} -162 q^{-107} +388 q^{-108} +1255 q^{-109} +707 q^{-110} -133 q^{-111} -1175 q^{-112} -853 q^{-113} -425 q^{-114} +327 q^{-115} +1413 q^{-116} +964 q^{-117} +11 q^{-118} -1256 q^{-119} -1040 q^{-120} -623 q^{-121} +315 q^{-122} +1556 q^{-123} +1178 q^{-124} +109 q^{-125} -1348 q^{-126} -1223 q^{-127} -800 q^{-128} +306 q^{-129} +1676 q^{-130} +1385 q^{-131} +244 q^{-132} -1359 q^{-133} -1377 q^{-134} -1002 q^{-135} +183 q^{-136} +1662 q^{-137} +1543 q^{-138} +467 q^{-139} -1164 q^{-140} -1371 q^{-141} -1168 q^{-142} -86 q^{-143} +1395 q^{-144} +1506 q^{-145} +681 q^{-146} -767 q^{-147} -1099 q^{-148} -1139 q^{-149} -358 q^{-150} +923 q^{-151} +1189 q^{-152} +713 q^{-153} -353 q^{-154} -653 q^{-155} -860 q^{-156} -451 q^{-157} +465 q^{-158} +722 q^{-159} +528 q^{-160} -103 q^{-161} -256 q^{-162} -483 q^{-163} -357 q^{-164} +181 q^{-165} +333 q^{-166} +280 q^{-167} -25 q^{-168} -37 q^{-169} -199 q^{-170} -207 q^{-171} +62 q^{-172} +113 q^{-173} +110 q^{-174} -18 q^{-175} +36 q^{-176} -58 q^{-177} -102 q^{-178} +25 q^{-179} +25 q^{-180} +33 q^{-181} -17 q^{-182} +38 q^{-183} -8 q^{-184} -46 q^{-185} +12 q^{-186} + q^{-187} +7 q^{-188} -12 q^{-189} +22 q^{-190} +2 q^{-191} -18 q^{-192} +7 q^{-193} -2 q^{-194} +2 q^{-195} -7 q^{-196} +8 q^{-197} +2 q^{-198} -7 q^{-199} +4 q^{-200} - q^{-201} + q^{-202} -2 q^{-203} + q^{-204} + q^{-205} -2 q^{-206} + q^{-207} </math> \|		coloured_jones_6 = <math> q^{-18} - q^{-19} + q^{-21} - q^{-24} +3 q^{-25} -3 q^{-26} -2 q^{-27} +4 q^{-28} +2 q^{-29} +2 q^{-30} -5 q^{-31} +6 q^{-32} -8 q^{-33} -10 q^{-34} +5 q^{-35} +7 q^{-36} +12 q^{-37} -4 q^{-38} +18 q^{-39} -15 q^{-40} -31 q^{-41} -11 q^{-42} +24 q^{-44} +8 q^{-45} +61 q^{-46} +4 q^{-47} -42 q^{-48} -48 q^{-49} -45 q^{-50} -7 q^{-51} -9 q^{-52} +124 q^{-53} +70 q^{-54} +16 q^{-55} -43 q^{-56} -89 q^{-57} -93 q^{-58} -120 q^{-59} +117 q^{-60} +113 q^{-61} +129 q^{-62} +64 q^{-63} -18 q^{-64} -129 q^{-65} -276 q^{-66} -5 q^{-67} +14 q^{-68} +156 q^{-69} +182 q^{-70} +185 q^{-71} +5 q^{-72} -308 q^{-73} -113 q^{-74} -206 q^{-75} -13 q^{-76} +126 q^{-77} +355 q^{-78} +253 q^{-79} -124 q^{-80} -26 q^{-81} -357 q^{-82} -291 q^{-83} -164 q^{-84} +313 q^{-85} +420 q^{-86} +167 q^{-87} +284 q^{-88} -282 q^{-89} -481 q^{-90} -558 q^{-91} +50 q^{-92} +373 q^{-93} +381 q^{-94} +683 q^{-95} +5 q^{-96} -478 q^{-97} -885 q^{-98} -304 q^{-99} +139 q^{-100} +440 q^{-101} +1024 q^{-102} +374 q^{-103} -325 q^{-104} -1077 q^{-105} -618 q^{-106} -162 q^{-107} +388 q^{-108} +1255 q^{-109} +707 q^{-110} -133 q^{-111} -1175 q^{-112} -853 q^{-113} -425 q^{-114} +327 q^{-115} +1413 q^{-116} +964 q^{-117} +11 q^{-118} -1256 q^{-119} -1040 q^{-120} -623 q^{-121} +315 q^{-122} +1556 q^{-123} +1178 q^{-124} +109 q^{-125} -1348 q^{-126} -1223 q^{-127} -800 q^{-128} +306 q^{-129} +1676 q^{-130} +1385 q^{-131} +244 q^{-132} -1359 q^{-133} -1377 q^{-134} -1002 q^{-135} +183 q^{-136} +1662 q^{-137} +1543 q^{-138} +467 q^{-139} -1164 q^{-140} -1371 q^{-141} -1168 q^{-142} -86 q^{-143} +1395 q^{-144} +1506 q^{-145} +681 q^{-146} -767 q^{-147} -1099 q^{-148} -1139 q^{-149} -358 q^{-150} +923 q^{-151} +1189 q^{-152} +713 q^{-153} -353 q^{-154} -653 q^{-155} -860 q^{-156} -451 q^{-157} +465 q^{-158} +722 q^{-159} +528 q^{-160} -103 q^{-161} -256 q^{-162} -483 q^{-163} -357 q^{-164} +181 q^{-165} +333 q^{-166} +280 q^{-167} -25 q^{-168} -37 q^{-169} -199 q^{-170} -207 q^{-171} +62 q^{-172} +113 q^{-173} +110 q^{-174} -18 q^{-175} +36 q^{-176} -58 q^{-177} -102 q^{-178} +25 q^{-179} +25 q^{-180} +33 q^{-181} -17 q^{-182} +38 q^{-183} -8 q^{-184} -46 q^{-185} +12 q^{-186} + q^{-187} +7 q^{-188} -12 q^{-189} +22 q^{-190} +2 q^{-191} -18 q^{-192} +7 q^{-193} -2 q^{-194} +2 q^{-195} -7 q^{-196} +8 q^{-197} +2 q^{-198} -7 q^{-199} +4 q^{-200} - q^{-201} + q^{-202} -2 q^{-203} + q^{-204} + q^{-205} -2 q^{-206} + q^{-207} </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, 9]]</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, 9]]</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[3, 12, 4, 13], X[7, 16, 8, 17], X[9, 18, 10, 1],		<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[3, 12, 4, 13], X[7, 16, 8, 17], X[9, 18, 10, 1],
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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[9, 9]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_9_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, 9]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_9_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, 9]]&) /@ {~~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, 9]]&) /@ {
			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, 2, {4, 6}, 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, 2, {4, 6}, 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[9, 9]][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, 9]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:41, 30 August 2005

2005-08-30T14:41:44Z

Show changes

DrorsRobot at 01:09, 30 August 2005

2005-08-30T01:09:46Z

← 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 22:09, 29 August 2005

2005-08-29T22:09:17Z

Show changes

ScottTestRobot at 00:16, 29 August 2005

2005-08-29T00:16:16Z

← 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=9\|k=9\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,8,-2,9,-7,1,-3,5,-4,6,-8,2,-9,7,-6,3,-5,4/goTop.html}}
	{\| align=left
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=9\|k=9\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,8,-2,9,-7,1,-3,5,-4,6,-8,2,-9,7,-6,3,-5,4/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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	<td width=14.2857%><table cellpadding=0 cellspacing=0>		<td width=14.2857%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>-23</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>1</td></tr>		<tr align=center><td>-23</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>1</td></tr>
	<tr align=center><td>-25</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>-25</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 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

2005-08-28T01:52:31Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T21:22:05Z

Resetting knot page to basic template.

New page

9 9 - 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 22:09, 29 August 2005

ScottTestRobot at 00:16, 29 August 2005

ScottTestRobot at 01:52, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.