ScottTestRobot at 22:04, 1 September 2005

2005-09-01T22:04:09Z

DrorsRobot at 22:52, 31 August 2005

2005-08-31T22:52:03Z

← Older revision		Revision as of 18:52, 31 August 2005
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	coloured_jones_4 = <math>q^{40}-4 q^{39}+4 q^{38}+5 q^{37}-12 q^{36}+5 q^{35}-12 q^{34}+32 q^{33}+22 q^{32}-82 q^{31}-q^{30}-22 q^{29}+169 q^{28}+110 q^{27}-320 q^{26}-143 q^{25}-63 q^{24}+615 q^{23}+473 q^{22}-800 q^{21}-714 q^{20}-375 q^{19}+1520 q^{18}+1528 q^{17}-1280 q^{16}-1950 q^{15}-1425 q^{14}+2619 q^{13}+3491 q^{12}-1172 q^{11}-3513 q^{10}-3439 q^9+3210 q^8+5875 q^7-126 q^6-4591 q^5-5888 q^4+2829 q^3+7705 q^2+1513 q-4619-7858 q^{-1} +1655 q^{-2} +8346 q^{-3} +3084 q^{-4} -3679 q^{-5} -8782 q^{-6} +153 q^{-7} +7773 q^{-8} +4205 q^{-9} -2126 q^{-10} -8618 q^{-11} -1359 q^{-12} +6248 q^{-13} +4757 q^{-14} -281 q^{-15} -7461 q^{-16} -2620 q^{-17} +4048 q^{-18} +4583 q^{-19} +1473 q^{-20} -5449 q^{-21} -3221 q^{-22} +1664 q^{-23} +3546 q^{-24} +2540 q^{-25} -3029 q^{-26} -2834 q^{-27} -158 q^{-28} +1950 q^{-29} +2512 q^{-30} -1016 q^{-31} -1717 q^{-32} -881 q^{-33} +550 q^{-34} +1659 q^{-35} +7 q^{-36} -623 q^{-37} -712 q^{-38} -119 q^{-39} +736 q^{-40} +192 q^{-41} -65 q^{-42} -308 q^{-43} -192 q^{-44} +215 q^{-45} +88 q^{-46} +51 q^{-47} -75 q^{-48} -88 q^{-49} +42 q^{-50} +15 q^{-51} +26 q^{-52} -8 q^{-53} -22 q^{-54} +6 q^{-55} +5 q^{-57} -3 q^{-59} + q^{-60} </math> \|		coloured_jones_4 = <math>q^{40}-4 q^{39}+4 q^{38}+5 q^{37}-12 q^{36}+5 q^{35}-12 q^{34}+32 q^{33}+22 q^{32}-82 q^{31}-q^{30}-22 q^{29}+169 q^{28}+110 q^{27}-320 q^{26}-143 q^{25}-63 q^{24}+615 q^{23}+473 q^{22}-800 q^{21}-714 q^{20}-375 q^{19}+1520 q^{18}+1528 q^{17}-1280 q^{16}-1950 q^{15}-1425 q^{14}+2619 q^{13}+3491 q^{12}-1172 q^{11}-3513 q^{10}-3439 q^9+3210 q^8+5875 q^7-126 q^6-4591 q^5-5888 q^4+2829 q^3+7705 q^2+1513 q-4619-7858 q^{-1} +1655 q^{-2} +8346 q^{-3} +3084 q^{-4} -3679 q^{-5} -8782 q^{-6} +153 q^{-7} +7773 q^{-8} +4205 q^{-9} -2126 q^{-10} -8618 q^{-11} -1359 q^{-12} +6248 q^{-13} +4757 q^{-14} -281 q^{-15} -7461 q^{-16} -2620 q^{-17} +4048 q^{-18} +4583 q^{-19} +1473 q^{-20} -5449 q^{-21} -3221 q^{-22} +1664 q^{-23} +3546 q^{-24} +2540 q^{-25} -3029 q^{-26} -2834 q^{-27} -158 q^{-28} +1950 q^{-29} +2512 q^{-30} -1016 q^{-31} -1717 q^{-32} -881 q^{-33} +550 q^{-34} +1659 q^{-35} +7 q^{-36} -623 q^{-37} -712 q^{-38} -119 q^{-39} +736 q^{-40} +192 q^{-41} -65 q^{-42} -308 q^{-43} -192 q^{-44} +215 q^{-45} +88 q^{-46} +51 q^{-47} -75 q^{-48} -88 q^{-49} +42 q^{-50} +15 q^{-51} +26 q^{-52} -8 q^{-53} -22 q^{-54} +6 q^{-55} +5 q^{-57} -3 q^{-59} + q^{-60} </math> \|
	coloured_jones_5 = <math>q^{60}-4 q^{59}+4 q^{58}+5 q^{57}-12 q^{56}+q^{55}+8 q^{54}+13 q^{52}-q^{51}-53 q^{50}-28 q^{49}+63 q^{48}+98 q^{47}+58 q^{46}-107 q^{45}-268 q^{44}-173 q^{43}+243 q^{42}+628 q^{41}+390 q^{40}-448 q^{39}-1214 q^{38}-955 q^{37}+629 q^{36}+2314 q^{35}+2043 q^{34}-760 q^{33}-3870 q^{32}-3950 q^{31}+379 q^{30}+5989 q^{29}+7057 q^{28}+788 q^{27}-8430 q^{26}-11461 q^{25}-3261 q^{24}+10649 q^{23}+17198 q^{22}+7522 q^{21}-12237 q^{20}-23812 q^{19}-13540 q^{18}+12335 q^{17}+30612 q^{16}+21362 q^{15}-10740 q^{14}-36811 q^{13}-30057 q^{12}+7035 q^{11}+41591 q^{10}+39116 q^9-1816 q^8-44414 q^7-47270 q^6-4751 q^5+45119 q^4+54206 q^3+11476 q^2-43822 q-58974-18273 q^{-1} +40926 q^{-2} +62017 q^{-3} +24100 q^{-4} -36876 q^{-5} -62884 q^{-6} -29276 q^{-7} +31978 q^{-8} +62395 q^{-9} +33340 q^{-10} -26575 q^{-11} -60287 q^{-12} -36755 q^{-13} +20653 q^{-14} +57144 q^{-15} +39304 q^{-16} -14307 q^{-17} -52724 q^{-18} -41185 q^{-19} +7582 q^{-20} +47206 q^{-21} +42059 q^{-22} -674 q^{-23} -40432 q^{-24} -41809 q^{-25} -6032 q^{-26} +32659 q^{-27} +40014 q^{-28} +11998 q^{-29} -24126 q^{-30} -36536 q^{-31} -16696 q^{-32} +15479 q^{-33} +31482 q^{-34} +19480 q^{-35} -7415 q^{-36} -25111 q^{-37} -20175 q^{-38} +607 q^{-39} +18265 q^{-40} +18798 q^{-41} +4212 q^{-42} -11549 q^{-43} -15802 q^{-44} -6997 q^{-45} +5868 q^{-46} +11967 q^{-47} +7727 q^{-48} -1657 q^{-49} -7988 q^{-50} -7003 q^{-51} -935 q^{-52} +4579 q^{-53} +5464 q^{-54} +2059 q^{-55} -2081 q^{-56} -3687 q^{-57} -2191 q^{-58} +535 q^{-59} +2177 q^{-60} +1772 q^{-61} +197 q^{-62} -1078 q^{-63} -1206 q^{-64} -412 q^{-65} +429 q^{-66} +691 q^{-67} +384 q^{-68} -103 q^{-69} -366 q^{-70} -251 q^{-71} - q^{-72} +138 q^{-73} +147 q^{-74} +48 q^{-75} -67 q^{-76} -73 q^{-77} -15 q^{-78} +9 q^{-79} +24 q^{-80} +26 q^{-81} -8 q^{-82} -15 q^{-83} - q^{-84} +5 q^{-87} -3 q^{-89} + q^{-90} </math> \|		coloured_jones_5 = <math>q^{60}-4 q^{59}+4 q^{58}+5 q^{57}-12 q^{56}+q^{55}+8 q^{54}+13 q^{52}-q^{51}-53 q^{50}-28 q^{49}+63 q^{48}+98 q^{47}+58 q^{46}-107 q^{45}-268 q^{44}-173 q^{43}+243 q^{42}+628 q^{41}+390 q^{40}-448 q^{39}-1214 q^{38}-955 q^{37}+629 q^{36}+2314 q^{35}+2043 q^{34}-760 q^{33}-3870 q^{32}-3950 q^{31}+379 q^{30}+5989 q^{29}+7057 q^{28}+788 q^{27}-8430 q^{26}-11461 q^{25}-3261 q^{24}+10649 q^{23}+17198 q^{22}+7522 q^{21}-12237 q^{20}-23812 q^{19}-13540 q^{18}+12335 q^{17}+30612 q^{16}+21362 q^{15}-10740 q^{14}-36811 q^{13}-30057 q^{12}+7035 q^{11}+41591 q^{10}+39116 q^9-1816 q^8-44414 q^7-47270 q^6-4751 q^5+45119 q^4+54206 q^3+11476 q^2-43822 q-58974-18273 q^{-1} +40926 q^{-2} +62017 q^{-3} +24100 q^{-4} -36876 q^{-5} -62884 q^{-6} -29276 q^{-7} +31978 q^{-8} +62395 q^{-9} +33340 q^{-10} -26575 q^{-11} -60287 q^{-12} -36755 q^{-13} +20653 q^{-14} +57144 q^{-15} +39304 q^{-16} -14307 q^{-17} -52724 q^{-18} -41185 q^{-19} +7582 q^{-20} +47206 q^{-21} +42059 q^{-22} -674 q^{-23} -40432 q^{-24} -41809 q^{-25} -6032 q^{-26} +32659 q^{-27} +40014 q^{-28} +11998 q^{-29} -24126 q^{-30} -36536 q^{-31} -16696 q^{-32} +15479 q^{-33} +31482 q^{-34} +19480 q^{-35} -7415 q^{-36} -25111 q^{-37} -20175 q^{-38} +607 q^{-39} +18265 q^{-40} +18798 q^{-41} +4212 q^{-42} -11549 q^{-43} -15802 q^{-44} -6997 q^{-45} +5868 q^{-46} +11967 q^{-47} +7727 q^{-48} -1657 q^{-49} -7988 q^{-50} -7003 q^{-51} -935 q^{-52} +4579 q^{-53} +5464 q^{-54} +2059 q^{-55} -2081 q^{-56} -3687 q^{-57} -2191 q^{-58} +535 q^{-59} +2177 q^{-60} +1772 q^{-61} +197 q^{-62} -1078 q^{-63} -1206 q^{-64} -412 q^{-65} +429 q^{-66} +691 q^{-67} +384 q^{-68} -103 q^{-69} -366 q^{-70} -251 q^{-71} - q^{-72} +138 q^{-73} +147 q^{-74} +48 q^{-75} -67 q^{-76} -73 q^{-77} -15 q^{-78} +9 q^{-79} +24 q^{-80} +26 q^{-81} -8 q^{-82} -15 q^{-83} - q^{-84} +5 q^{-87} -3 q^{-89} + q^{-90} </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[10, 60]]</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, 60]]</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[10, 6, 11, 5], X[8, 3, 9, 4], X[2, 9, 3, 10],		<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[10, 6, 11, 5], X[8, 3, 9, 4], X[2, 9, 3, 10],
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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>5</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>5</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, 60]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_60_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, 60]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_60_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, 60]]&) /@ {~~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, 60]]&) /@ {
			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, 60]][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, 60]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:40, 30 August 2005

2005-08-30T14:40:13Z

Show changes

DrorsRobot at 01:07, 30 August 2005

2005-08-30T01:07:53Z

← Older revision		Revision as of 21:07, 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 22:18, 29 August 2005

2005-08-29T22:18:02Z

Show changes

ScottTestRobot at 00:14, 29 August 2005

2005-08-29T00:14:08Z

← Older revision		Revision as of 20:14, 28 August 2005
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			<!-- -->
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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=60\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-1,2,-7,6,-3,4,-2,5,-10,9,-6,7,-5,8,-9,10,-8/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=60\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-1,2,-7,6,-3,4,-2,5,-10,9,-6,7,-5,8,-9,10,-8/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=13.3333%><table cellpadding=0 cellspacing=0>		<td width=13.3333%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>-11</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> </td><td>-2</td></tr>		<tr align=center><td>-11</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> </td><td>-2</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> </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> </td><td> </td><td>1</td></tr>
	</table>~~</center>~~		</table>}}

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

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	q t + 3 q t + q t</nowiki></pre></td></tr>		q t + 3 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:50, 28 August 2005

2005-08-28T01:50:36Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:12Z

Resetting knot page to basic template.

New page

10 60 - Revision history

ScottTestRobot at 22:04, 1 September 2005

DrorsRobot at 22:52, 31 August 2005

ScottKnotPageRobot at 14:40, 30 August 2005

DrorsRobot at 01:07, 30 August 2005

DrorsRobot at 22:18, 29 August 2005

ScottTestRobot at 00:14, 29 August 2005

ScottTestRobot at 01:50, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.