10 148 - Revision history

Drorbn: Reverted edits by CnaacElget (Talk); changed back to last version by ScottTestRobot

2009-05-28T03:30:00Z

Reverted edits by CnaacElget (Talk); changed back to last version by ScottTestRobot

← Older revision		Revision as of 23:30, 27 May 2009
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CnaacElget at 09:03, 27 May 2009

2009-05-27T09:03:16Z

← Older revision		Revision as of 05:03, 27 May 2009
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CnaacElget at 12:10, 26 May 2009

2009-05-26T12:10:52Z

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CnaacElget at 20:57, 22 May 2009

2009-05-22T20:57:55Z

← Older revision		Revision as of 16:57, 22 May 2009
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ScottTestRobot at 22:00, 1 September 2005

2005-09-01T22:00:16Z

Show changes

DrorsRobot at 22:44, 31 August 2005

2005-08-31T22:44:58Z

← Older revision		Revision as of 18:44, 31 August 2005
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	coloured_jones_5 = <math>-2 q^{11}+5 q^9+5 q^8-4 q^6-21 q^5-18 q^4+11 q^3+39 q^2+47 q+20-51 q^{-1} -114 q^{-2} -84 q^{-3} +32 q^{-4} +174 q^{-5} +205 q^{-6} +65 q^{-7} -199 q^{-8} -381 q^{-9} -245 q^{-10} +162 q^{-11} +526 q^{-12} +518 q^{-13} +15 q^{-14} -649 q^{-15} -840 q^{-16} -265 q^{-17} +645 q^{-18} +1145 q^{-19} +637 q^{-20} -568 q^{-21} -1394 q^{-22} -1000 q^{-23} +373 q^{-24} +1555 q^{-25} +1363 q^{-26} -164 q^{-27} -1622 q^{-28} -1615 q^{-29} -100 q^{-30} +1622 q^{-31} +1836 q^{-32} +267 q^{-33} -1562 q^{-34} -1915 q^{-35} -467 q^{-36} +1485 q^{-37} +2002 q^{-38} +548 q^{-39} -1396 q^{-40} -1971 q^{-41} -673 q^{-42} +1293 q^{-43} +1982 q^{-44} +721 q^{-45} -1179 q^{-46} -1904 q^{-47} -825 q^{-48} +1023 q^{-49} +1852 q^{-50} +899 q^{-51} -833 q^{-52} -1718 q^{-53} -1008 q^{-54} +586 q^{-55} +1564 q^{-56} +1081 q^{-57} -302 q^{-58} -1325 q^{-59} -1127 q^{-60} + q^{-61} +1031 q^{-62} +1103 q^{-63} +264 q^{-64} -685 q^{-65} -979 q^{-66} -476 q^{-67} +338 q^{-68} +784 q^{-69} +566 q^{-70} -44 q^{-71} -509 q^{-72} -551 q^{-73} -182 q^{-74} +266 q^{-75} +436 q^{-76} +263 q^{-77} -42 q^{-78} -270 q^{-79} -277 q^{-80} -73 q^{-81} +126 q^{-82} +191 q^{-83} +124 q^{-84} -18 q^{-85} -112 q^{-86} -103 q^{-87} -31 q^{-88} +40 q^{-89} +70 q^{-90} +36 q^{-91} -9 q^{-92} -26 q^{-93} -29 q^{-94} -8 q^{-95} +15 q^{-96} +14 q^{-97} + q^{-99} -4 q^{-100} -7 q^{-101} +3 q^{-102} +4 q^{-103} -2 q^{-104} + q^{-106} -2 q^{-107} +2 q^{-109} - q^{-110} </math> \|		coloured_jones_5 = <math>-2 q^{11}+5 q^9+5 q^8-4 q^6-21 q^5-18 q^4+11 q^3+39 q^2+47 q+20-51 q^{-1} -114 q^{-2} -84 q^{-3} +32 q^{-4} +174 q^{-5} +205 q^{-6} +65 q^{-7} -199 q^{-8} -381 q^{-9} -245 q^{-10} +162 q^{-11} +526 q^{-12} +518 q^{-13} +15 q^{-14} -649 q^{-15} -840 q^{-16} -265 q^{-17} +645 q^{-18} +1145 q^{-19} +637 q^{-20} -568 q^{-21} -1394 q^{-22} -1000 q^{-23} +373 q^{-24} +1555 q^{-25} +1363 q^{-26} -164 q^{-27} -1622 q^{-28} -1615 q^{-29} -100 q^{-30} +1622 q^{-31} +1836 q^{-32} +267 q^{-33} -1562 q^{-34} -1915 q^{-35} -467 q^{-36} +1485 q^{-37} +2002 q^{-38} +548 q^{-39} -1396 q^{-40} -1971 q^{-41} -673 q^{-42} +1293 q^{-43} +1982 q^{-44} +721 q^{-45} -1179 q^{-46} -1904 q^{-47} -825 q^{-48} +1023 q^{-49} +1852 q^{-50} +899 q^{-51} -833 q^{-52} -1718 q^{-53} -1008 q^{-54} +586 q^{-55} +1564 q^{-56} +1081 q^{-57} -302 q^{-58} -1325 q^{-59} -1127 q^{-60} + q^{-61} +1031 q^{-62} +1103 q^{-63} +264 q^{-64} -685 q^{-65} -979 q^{-66} -476 q^{-67} +338 q^{-68} +784 q^{-69} +566 q^{-70} -44 q^{-71} -509 q^{-72} -551 q^{-73} -182 q^{-74} +266 q^{-75} +436 q^{-76} +263 q^{-77} -42 q^{-78} -270 q^{-79} -277 q^{-80} -73 q^{-81} +126 q^{-82} +191 q^{-83} +124 q^{-84} -18 q^{-85} -112 q^{-86} -103 q^{-87} -31 q^{-88} +40 q^{-89} +70 q^{-90} +36 q^{-91} -9 q^{-92} -26 q^{-93} -29 q^{-94} -8 q^{-95} +15 q^{-96} +14 q^{-97} + q^{-99} -4 q^{-100} -7 q^{-101} +3 q^{-102} +4 q^{-103} -2 q^{-104} + q^{-106} -2 q^{-107} +2 q^{-109} - q^{-110} </math> \|
	coloured_jones_6 = <math>q^{20}-q^{19}-q^{18}-2 q^{15}-3 q^{14}+9 q^{13}+8 q^{12}+6 q^{11}+3 q^{10}-8 q^9-32 q^8-49 q^7-11 q^6+37 q^5+76 q^4+107 q^3+81 q^2-54 q-212-251 q^{-1} -148 q^{-2} +46 q^{-3} +356 q^{-4} +563 q^{-5} +391 q^{-6} -128 q^{-7} -660 q^{-8} -909 q^{-9} -781 q^{-10} +87 q^{-11} +1168 q^{-12} +1681 q^{-13} +1119 q^{-14} -241 q^{-15} -1699 q^{-16} -2671 q^{-17} -1725 q^{-18} +607 q^{-19} +2936 q^{-20} +3550 q^{-21} +2003 q^{-22} -1060 q^{-23} -4410 q^{-24} -4761 q^{-25} -1916 q^{-26} +2652 q^{-27} +5678 q^{-28} +5367 q^{-29} +1472 q^{-30} -4559 q^{-31} -7328 q^{-32} -5327 q^{-33} +674 q^{-34} +6208 q^{-35} +8079 q^{-36} +4586 q^{-37} -3208 q^{-38} -8316 q^{-39} -7915 q^{-40} -1660 q^{-41} +5398 q^{-42} +9250 q^{-43} +6793 q^{-44} -1573 q^{-45} -8066 q^{-46} -9068 q^{-47} -3214 q^{-48} +4294 q^{-49} +9296 q^{-50} +7768 q^{-51} -457 q^{-52} -7437 q^{-53} -9266 q^{-54} -3926 q^{-55} +3449 q^{-56} +8936 q^{-57} +8032 q^{-58} +232 q^{-59} -6790 q^{-60} -9112 q^{-61} -4331 q^{-62} +2667 q^{-63} +8400 q^{-64} +8112 q^{-65} +1020 q^{-66} -5874 q^{-67} -8752 q^{-68} -4884 q^{-69} +1435 q^{-70} +7406 q^{-71} +8086 q^{-72} +2280 q^{-73} -4206 q^{-74} -7852 q^{-75} -5545 q^{-76} -520 q^{-77} +5480 q^{-78} +7506 q^{-79} +3776 q^{-80} -1639 q^{-81} -5888 q^{-82} -5631 q^{-83} -2706 q^{-84} +2560 q^{-85} +5710 q^{-86} +4541 q^{-87} +1092 q^{-88} -2865 q^{-89} -4317 q^{-90} -3881 q^{-91} -403 q^{-92} +2775 q^{-93} +3644 q^{-94} +2560 q^{-95} +60 q^{-96} -1815 q^{-97} -3153 q^{-98} -1883 q^{-99} +69 q^{-100} +1521 q^{-101} +2042 q^{-102} +1371 q^{-103} +334 q^{-104} -1286 q^{-105} -1432 q^{-106} -981 q^{-107} -163 q^{-108} +596 q^{-109} +947 q^{-110} +930 q^{-111} +32 q^{-112} -330 q^{-113} -591 q^{-114} -503 q^{-115} -233 q^{-116} +150 q^{-117} +479 q^{-118} +238 q^{-119} +164 q^{-120} -59 q^{-121} -172 q^{-122} -239 q^{-123} -113 q^{-124} +89 q^{-125} +45 q^{-126} +113 q^{-127} +59 q^{-128} +19 q^{-129} -70 q^{-130} -60 q^{-131} +9 q^{-132} -23 q^{-133} +19 q^{-134} +19 q^{-135} +25 q^{-136} -13 q^{-137} -13 q^{-138} +10 q^{-139} -11 q^{-140} +9 q^{-143} -4 q^{-144} -5 q^{-145} +6 q^{-146} -2 q^{-147} - q^{-149} +2 q^{-150} -2 q^{-152} + q^{-153} </math> \|		coloured_jones_6 = <math>q^{20}-q^{19}-q^{18}-2 q^{15}-3 q^{14}+9 q^{13}+8 q^{12}+6 q^{11}+3 q^{10}-8 q^9-32 q^8-49 q^7-11 q^6+37 q^5+76 q^4+107 q^3+81 q^2-54 q-212-251 q^{-1} -148 q^{-2} +46 q^{-3} +356 q^{-4} +563 q^{-5} +391 q^{-6} -128 q^{-7} -660 q^{-8} -909 q^{-9} -781 q^{-10} +87 q^{-11} +1168 q^{-12} +1681 q^{-13} +1119 q^{-14} -241 q^{-15} -1699 q^{-16} -2671 q^{-17} -1725 q^{-18} +607 q^{-19} +2936 q^{-20} +3550 q^{-21} +2003 q^{-22} -1060 q^{-23} -4410 q^{-24} -4761 q^{-25} -1916 q^{-26} +2652 q^{-27} +5678 q^{-28} +5367 q^{-29} +1472 q^{-30} -4559 q^{-31} -7328 q^{-32} -5327 q^{-33} +674 q^{-34} +6208 q^{-35} +8079 q^{-36} +4586 q^{-37} -3208 q^{-38} -8316 q^{-39} -7915 q^{-40} -1660 q^{-41} +5398 q^{-42} +9250 q^{-43} +6793 q^{-44} -1573 q^{-45} -8066 q^{-46} -9068 q^{-47} -3214 q^{-48} +4294 q^{-49} +9296 q^{-50} +7768 q^{-51} -457 q^{-52} -7437 q^{-53} -9266 q^{-54} -3926 q^{-55} +3449 q^{-56} +8936 q^{-57} +8032 q^{-58} +232 q^{-59} -6790 q^{-60} -9112 q^{-61} -4331 q^{-62} +2667 q^{-63} +8400 q^{-64} +8112 q^{-65} +1020 q^{-66} -5874 q^{-67} -8752 q^{-68} -4884 q^{-69} +1435 q^{-70} +7406 q^{-71} +8086 q^{-72} +2280 q^{-73} -4206 q^{-74} -7852 q^{-75} -5545 q^{-76} -520 q^{-77} +5480 q^{-78} +7506 q^{-79} +3776 q^{-80} -1639 q^{-81} -5888 q^{-82} -5631 q^{-83} -2706 q^{-84} +2560 q^{-85} +5710 q^{-86} +4541 q^{-87} +1092 q^{-88} -2865 q^{-89} -4317 q^{-90} -3881 q^{-91} -403 q^{-92} +2775 q^{-93} +3644 q^{-94} +2560 q^{-95} +60 q^{-96} -1815 q^{-97} -3153 q^{-98} -1883 q^{-99} +69 q^{-100} +1521 q^{-101} +2042 q^{-102} +1371 q^{-103} +334 q^{-104} -1286 q^{-105} -1432 q^{-106} -981 q^{-107} -163 q^{-108} +596 q^{-109} +947 q^{-110} +930 q^{-111} +32 q^{-112} -330 q^{-113} -591 q^{-114} -503 q^{-115} -233 q^{-116} +150 q^{-117} +479 q^{-118} +238 q^{-119} +164 q^{-120} -59 q^{-121} -172 q^{-122} -239 q^{-123} -113 q^{-124} +89 q^{-125} +45 q^{-126} +113 q^{-127} +59 q^{-128} +19 q^{-129} -70 q^{-130} -60 q^{-131} +9 q^{-132} -23 q^{-133} +19 q^{-134} +19 q^{-135} +25 q^{-136} -13 q^{-137} -13 q^{-138} +10 q^{-139} -11 q^{-140} +9 q^{-143} -4 q^{-144} -5 q^{-145} +6 q^{-146} -2 q^{-147} - q^{-149} +2 q^{-150} -2 q^{-152} + q^{-153} </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, 148]]</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, 148]]</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[5, 12, 6, 13], 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[4, 2, 5, 1], X[8, 4, 9, 3], X[5, 12, 6, 13], 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, 148]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_148_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, 148]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_148_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, 148]]&) /@ {~~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, 148]]&) /@ {
			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, 148]][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, 148]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:36, 30 August 2005

2005-08-30T14:36:06Z

Show changes

DrorsRobot at 01:03, 30 August 2005

2005-08-30T01:03:25Z

← Older revision		Revision as of 21:03, 29 August 2005
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	</table>		</table>

			{\| 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

2005-08-29T22:26:07Z

Show changes

ScottTestRobot at 00:09, 29 August 2005

2005-08-29T00:09:11Z

← Older revision		Revision as of 20:09, 28 August 2005
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	<span id="top"></span>		<span id="top"></span>
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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=148\|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=148\|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}}
	\|}

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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>-15</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>-15</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>-17</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>-17</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 q t q t q t</nowiki></pre></td></tr>		q t q t q t q t q t q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]