ScottTestRobot at 22:00, 1 September 2005

2005-09-01T22:00:32Z

DrorsRobot at 22:45, 31 August 2005

2005-08-31T22:45:19Z

← Older revision		Revision as of 18:45, 31 August 2005
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	coloured_jones_5 = <math>2 q^{-4} +2 q^{-6} -3 q^{-7} -9 q^{-8} -9 q^{-9} +9 q^{-10} +11 q^{-11} +31 q^{-12} +25 q^{-13} -32 q^{-14} -73 q^{-15} -57 q^{-16} -17 q^{-17} +100 q^{-18} +196 q^{-19} +100 q^{-20} -111 q^{-21} -277 q^{-22} -325 q^{-23} -41 q^{-24} +409 q^{-25} +594 q^{-26} +303 q^{-27} -313 q^{-28} -904 q^{-29} -803 q^{-30} +93 q^{-31} +1076 q^{-32} +1353 q^{-33} +491 q^{-34} -1084 q^{-35} -1958 q^{-36} -1191 q^{-37} +743 q^{-38} +2379 q^{-39} +2157 q^{-40} -183 q^{-41} -2650 q^{-42} -2986 q^{-43} -682 q^{-44} +2585 q^{-45} +3864 q^{-46} +1611 q^{-47} -2368 q^{-48} -4448 q^{-49} -2586 q^{-50} +1894 q^{-51} +4953 q^{-52} +3466 q^{-53} -1410 q^{-54} -5204 q^{-55} -4234 q^{-56} +870 q^{-57} +5365 q^{-58} +4853 q^{-59} -384 q^{-60} -5409 q^{-61} -5339 q^{-62} -65 q^{-63} +5381 q^{-64} +5713 q^{-65} +490 q^{-66} -5288 q^{-67} -5985 q^{-68} -898 q^{-69} +5063 q^{-70} +6180 q^{-71} +1348 q^{-72} -4746 q^{-73} -6226 q^{-74} -1810 q^{-75} +4196 q^{-76} +6146 q^{-77} +2307 q^{-78} -3525 q^{-79} -5816 q^{-80} -2713 q^{-81} +2612 q^{-82} +5272 q^{-83} +3034 q^{-84} -1697 q^{-85} -4455 q^{-86} -3094 q^{-87} +745 q^{-88} +3485 q^{-89} +2936 q^{-90} +4 q^{-91} -2461 q^{-92} -2504 q^{-93} -525 q^{-94} +1518 q^{-95} +1938 q^{-96} +745 q^{-97} -764 q^{-98} -1339 q^{-99} -736 q^{-100} +277 q^{-101} +809 q^{-102} +572 q^{-103} -7 q^{-104} -418 q^{-105} -394 q^{-106} -73 q^{-107} +188 q^{-108} +217 q^{-109} +73 q^{-110} -61 q^{-111} -107 q^{-112} -56 q^{-113} +24 q^{-114} +50 q^{-115} +20 q^{-116} -9 q^{-117} -10 q^{-118} -14 q^{-119} -2 q^{-120} +15 q^{-121} + q^{-122} -6 q^{-123} + q^{-124} -3 q^{-126} +4 q^{-127} + q^{-128} -3 q^{-129} + q^{-130} </math> \|		coloured_jones_5 = <math>2 q^{-4} +2 q^{-6} -3 q^{-7} -9 q^{-8} -9 q^{-9} +9 q^{-10} +11 q^{-11} +31 q^{-12} +25 q^{-13} -32 q^{-14} -73 q^{-15} -57 q^{-16} -17 q^{-17} +100 q^{-18} +196 q^{-19} +100 q^{-20} -111 q^{-21} -277 q^{-22} -325 q^{-23} -41 q^{-24} +409 q^{-25} +594 q^{-26} +303 q^{-27} -313 q^{-28} -904 q^{-29} -803 q^{-30} +93 q^{-31} +1076 q^{-32} +1353 q^{-33} +491 q^{-34} -1084 q^{-35} -1958 q^{-36} -1191 q^{-37} +743 q^{-38} +2379 q^{-39} +2157 q^{-40} -183 q^{-41} -2650 q^{-42} -2986 q^{-43} -682 q^{-44} +2585 q^{-45} +3864 q^{-46} +1611 q^{-47} -2368 q^{-48} -4448 q^{-49} -2586 q^{-50} +1894 q^{-51} +4953 q^{-52} +3466 q^{-53} -1410 q^{-54} -5204 q^{-55} -4234 q^{-56} +870 q^{-57} +5365 q^{-58} +4853 q^{-59} -384 q^{-60} -5409 q^{-61} -5339 q^{-62} -65 q^{-63} +5381 q^{-64} +5713 q^{-65} +490 q^{-66} -5288 q^{-67} -5985 q^{-68} -898 q^{-69} +5063 q^{-70} +6180 q^{-71} +1348 q^{-72} -4746 q^{-73} -6226 q^{-74} -1810 q^{-75} +4196 q^{-76} +6146 q^{-77} +2307 q^{-78} -3525 q^{-79} -5816 q^{-80} -2713 q^{-81} +2612 q^{-82} +5272 q^{-83} +3034 q^{-84} -1697 q^{-85} -4455 q^{-86} -3094 q^{-87} +745 q^{-88} +3485 q^{-89} +2936 q^{-90} +4 q^{-91} -2461 q^{-92} -2504 q^{-93} -525 q^{-94} +1518 q^{-95} +1938 q^{-96} +745 q^{-97} -764 q^{-98} -1339 q^{-99} -736 q^{-100} +277 q^{-101} +809 q^{-102} +572 q^{-103} -7 q^{-104} -418 q^{-105} -394 q^{-106} -73 q^{-107} +188 q^{-108} +217 q^{-109} +73 q^{-110} -61 q^{-111} -107 q^{-112} -56 q^{-113} +24 q^{-114} +50 q^{-115} +20 q^{-116} -9 q^{-117} -10 q^{-118} -14 q^{-119} -2 q^{-120} +15 q^{-121} + q^{-122} -6 q^{-123} + q^{-124} -3 q^{-126} +4 q^{-127} + q^{-128} -3 q^{-129} + q^{-130} </math> \|
	coloured_jones_6 = <math> q^{-3} +2 q^{-4} -4 q^{-7} -6 q^{-8} -12 q^{-9} -4 q^{-10} +17 q^{-11} +32 q^{-12} +32 q^{-13} +15 q^{-14} -9 q^{-15} -94 q^{-16} -118 q^{-17} -75 q^{-18} +58 q^{-19} +172 q^{-20} +246 q^{-21} +273 q^{-22} -47 q^{-23} -367 q^{-24} -607 q^{-25} -442 q^{-26} -78 q^{-27} +538 q^{-28} +1223 q^{-29} +991 q^{-30} +217 q^{-31} -1065 q^{-32} -1748 q^{-33} -1913 q^{-34} -686 q^{-35} +1687 q^{-36} +3033 q^{-37} +3045 q^{-38} +790 q^{-39} -1890 q^{-40} -4813 q^{-41} -4841 q^{-42} -1208 q^{-43} +3236 q^{-44} +6832 q^{-45} +6177 q^{-46} +2410 q^{-47} -5114 q^{-48} -9796 q^{-49} -8228 q^{-50} -1777 q^{-51} +7270 q^{-52} +12173 q^{-53} +11251 q^{-54} +383 q^{-55} -10932 q^{-56} -15783 q^{-57} -11376 q^{-58} +1632 q^{-59} +14200 q^{-60} +20532 q^{-61} +10341 q^{-62} -6174 q^{-63} -19536 q^{-64} -21236 q^{-65} -8119 q^{-66} +10875 q^{-67} +26268 q^{-68} +20425 q^{-69} +2105 q^{-70} -18630 q^{-71} -27853 q^{-72} -17790 q^{-73} +4709 q^{-74} +27892 q^{-75} +27584 q^{-76} +10132 q^{-77} -15352 q^{-78} -30885 q^{-79} -24815 q^{-80} -1144 q^{-81} +27269 q^{-82} +31596 q^{-83} +15978 q^{-84} -12047 q^{-85} -31830 q^{-86} -29176 q^{-87} -5473 q^{-88} +26000 q^{-89} +33694 q^{-90} +19989 q^{-91} -9201 q^{-92} -31763 q^{-93} -32050 q^{-94} -9069 q^{-95} +24016 q^{-96} +34648 q^{-97} +23419 q^{-98} -5642 q^{-99} -30221 q^{-100} -33983 q^{-101} -13285 q^{-102} +19844 q^{-103} +33650 q^{-104} +26588 q^{-105} -7 q^{-106} -25487 q^{-107} -33750 q^{-108} -18087 q^{-109} +12234 q^{-110} +28704 q^{-111} +27725 q^{-112} +7113 q^{-113} -16533 q^{-114} -29031 q^{-115} -20983 q^{-116} +2559 q^{-117} +19069 q^{-118} +24136 q^{-119} +12338 q^{-120} -5598 q^{-121} -19428 q^{-122} -18904 q^{-123} -4878 q^{-124} +7799 q^{-125} +15768 q^{-126} +12298 q^{-127} +2399 q^{-128} -8654 q^{-129} -12184 q^{-130} -6688 q^{-131} -4 q^{-132} +6715 q^{-133} +7780 q^{-134} +4589 q^{-135} -1590 q^{-136} -5099 q^{-137} -4210 q^{-138} -2288 q^{-139} +1251 q^{-140} +2980 q^{-141} +2969 q^{-142} +620 q^{-143} -1136 q^{-144} -1398 q^{-145} -1474 q^{-146} -310 q^{-147} +553 q^{-148} +1100 q^{-149} +454 q^{-150} -41 q^{-151} -151 q^{-152} -481 q^{-153} -245 q^{-154} -22 q^{-155} +276 q^{-156} +100 q^{-157} +18 q^{-158} +59 q^{-159} -94 q^{-160} -64 q^{-161} -35 q^{-162} +68 q^{-163} - q^{-164} -10 q^{-165} +30 q^{-166} -15 q^{-167} -8 q^{-168} -12 q^{-169} +22 q^{-170} -4 q^{-171} -10 q^{-172} +9 q^{-173} -3 q^{-174} -3 q^{-176} +4 q^{-177} + q^{-178} -3 q^{-179} + q^{-180} </math> \|		coloured_jones_6 = <math> q^{-3} +2 q^{-4} -4 q^{-7} -6 q^{-8} -12 q^{-9} -4 q^{-10} +17 q^{-11} +32 q^{-12} +32 q^{-13} +15 q^{-14} -9 q^{-15} -94 q^{-16} -118 q^{-17} -75 q^{-18} +58 q^{-19} +172 q^{-20} +246 q^{-21} +273 q^{-22} -47 q^{-23} -367 q^{-24} -607 q^{-25} -442 q^{-26} -78 q^{-27} +538 q^{-28} +1223 q^{-29} +991 q^{-30} +217 q^{-31} -1065 q^{-32} -1748 q^{-33} -1913 q^{-34} -686 q^{-35} +1687 q^{-36} +3033 q^{-37} +3045 q^{-38} +790 q^{-39} -1890 q^{-40} -4813 q^{-41} -4841 q^{-42} -1208 q^{-43} +3236 q^{-44} +6832 q^{-45} +6177 q^{-46} +2410 q^{-47} -5114 q^{-48} -9796 q^{-49} -8228 q^{-50} -1777 q^{-51} +7270 q^{-52} +12173 q^{-53} +11251 q^{-54} +383 q^{-55} -10932 q^{-56} -15783 q^{-57} -11376 q^{-58} +1632 q^{-59} +14200 q^{-60} +20532 q^{-61} +10341 q^{-62} -6174 q^{-63} -19536 q^{-64} -21236 q^{-65} -8119 q^{-66} +10875 q^{-67} +26268 q^{-68} +20425 q^{-69} +2105 q^{-70} -18630 q^{-71} -27853 q^{-72} -17790 q^{-73} +4709 q^{-74} +27892 q^{-75} +27584 q^{-76} +10132 q^{-77} -15352 q^{-78} -30885 q^{-79} -24815 q^{-80} -1144 q^{-81} +27269 q^{-82} +31596 q^{-83} +15978 q^{-84} -12047 q^{-85} -31830 q^{-86} -29176 q^{-87} -5473 q^{-88} +26000 q^{-89} +33694 q^{-90} +19989 q^{-91} -9201 q^{-92} -31763 q^{-93} -32050 q^{-94} -9069 q^{-95} +24016 q^{-96} +34648 q^{-97} +23419 q^{-98} -5642 q^{-99} -30221 q^{-100} -33983 q^{-101} -13285 q^{-102} +19844 q^{-103} +33650 q^{-104} +26588 q^{-105} -7 q^{-106} -25487 q^{-107} -33750 q^{-108} -18087 q^{-109} +12234 q^{-110} +28704 q^{-111} +27725 q^{-112} +7113 q^{-113} -16533 q^{-114} -29031 q^{-115} -20983 q^{-116} +2559 q^{-117} +19069 q^{-118} +24136 q^{-119} +12338 q^{-120} -5598 q^{-121} -19428 q^{-122} -18904 q^{-123} -4878 q^{-124} +7799 q^{-125} +15768 q^{-126} +12298 q^{-127} +2399 q^{-128} -8654 q^{-129} -12184 q^{-130} -6688 q^{-131} -4 q^{-132} +6715 q^{-133} +7780 q^{-134} +4589 q^{-135} -1590 q^{-136} -5099 q^{-137} -4210 q^{-138} -2288 q^{-139} +1251 q^{-140} +2980 q^{-141} +2969 q^{-142} +620 q^{-143} -1136 q^{-144} -1398 q^{-145} -1474 q^{-146} -310 q^{-147} +553 q^{-148} +1100 q^{-149} +454 q^{-150} -41 q^{-151} -151 q^{-152} -481 q^{-153} -245 q^{-154} -22 q^{-155} +276 q^{-156} +100 q^{-157} +18 q^{-158} +59 q^{-159} -94 q^{-160} -64 q^{-161} -35 q^{-162} +68 q^{-163} - q^{-164} -10 q^{-165} +30 q^{-166} -15 q^{-167} -8 q^{-168} -12 q^{-169} +22 q^{-170} -4 q^{-171} -10 q^{-172} +9 q^{-173} -3 q^{-174} -3 q^{-176} +4 q^{-177} + q^{-178} -3 q^{-179} + q^{-180} </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, 149]]</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, 149]]</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, 8, 4, 9], X[12, 6, 13, 5], X[13, 18, 14, 19],		<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, 8, 4, 9], X[12, 6, 13, 5], X[13, 18, 14, 19],
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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, 149]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_149_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, 149]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_149_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, 149]]&) /@ {~~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, 149]]&) /@ {
			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>{Chiral, 2, 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>{Chiral, 2, 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, 149]][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, 149]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:36, 30 August 2005

2005-08-30T14:36:26Z

Show changes

DrorsRobot at 01:03, 30 August 2005

2005-08-30T01:03:42Z

← Older revision		Revision as of 21:03, 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 22:26, 29 August 2005

2005-08-29T22:26:13Z

Show changes

ScottTestRobot at 00:09, 29 August 2005

2005-08-29T00:09:34Z

← Older revision		Revision as of 20:09, 28 August 2005
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			<!-- -->

			<!-- -->
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	<!-- provide an anchor so we can return to the top of the page -->		<!-- provide an anchor so we can return to the top of the page -->
	<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=149\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,3,-9,-10,2,-5,6,9,-3,-4,8,-7,5,-6,4,-8,7/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=149\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,3,-9,-10,2,-5,6,9,-3,-4,8,-7,5,-6,4,-8,7/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>-19</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>-2</td></tr>		<tr align=center><td>-19</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>-2</td></tr>
	<tr align=center><td>-21</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>-21</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 01:46, 28 August 2005

2005-08-28T01:46:49Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:35Z

Resetting knot page to basic template.

New page

10 149 - Revision history

ScottTestRobot at 22:00, 1 September 2005

DrorsRobot at 22:45, 31 August 2005

ScottKnotPageRobot at 14:36, 30 August 2005

DrorsRobot at 01:03, 30 August 2005

DrorsRobot at 22:26, 29 August 2005

ScottTestRobot at 00:09, 29 August 2005

ScottTestRobot at 01:46, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.