ScottTestRobot at 22:03, 1 September 2005

2005-09-01T22:03:28Z

DrorsRobot at 22:50, 31 August 2005

2005-08-31T22:50:28Z

← Older revision		Revision as of 18:50, 31 August 2005
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	coloured_jones_4 = <math>q^{40}-2 q^{39}+q^{38}+q^{37}-3 q^{36}+5 q^{35}-7 q^{34}+5 q^{33}+6 q^{32}-15 q^{31}+9 q^{30}-18 q^{29}+27 q^{28}+31 q^{27}-49 q^{26}-13 q^{25}-59 q^{24}+87 q^{23}+126 q^{22}-73 q^{21}-86 q^{20}-213 q^{19}+140 q^{18}+337 q^{17}+7 q^{16}-163 q^{15}-517 q^{14}+89 q^{13}+591 q^{12}+229 q^{11}-139 q^{10}-875 q^9-102 q^8+759 q^7+506 q^6+4 q^5-1137 q^4-336 q^3+780 q^2+705 q+197-1231 q^{-1} -511 q^{-2} +680 q^{-3} +774 q^{-4} +373 q^{-5} -1163 q^{-6} -603 q^{-7} +492 q^{-8} +734 q^{-9} +523 q^{-10} -959 q^{-11} -626 q^{-12} +241 q^{-13} +596 q^{-14} +626 q^{-15} -637 q^{-16} -564 q^{-17} -32 q^{-18} +366 q^{-19} +632 q^{-20} -282 q^{-21} -396 q^{-22} -210 q^{-23} +107 q^{-24} +494 q^{-25} -25 q^{-26} -169 q^{-27} -221 q^{-28} -68 q^{-29} +275 q^{-30} +61 q^{-31} -8 q^{-32} -123 q^{-33} -101 q^{-34} +102 q^{-35} +39 q^{-36} +35 q^{-37} -37 q^{-38} -57 q^{-39} +25 q^{-40} +8 q^{-41} +20 q^{-42} -4 q^{-43} -18 q^{-44} +4 q^{-45} +5 q^{-47} -3 q^{-49} + q^{-50} </math> \|		coloured_jones_4 = <math>q^{40}-2 q^{39}+q^{38}+q^{37}-3 q^{36}+5 q^{35}-7 q^{34}+5 q^{33}+6 q^{32}-15 q^{31}+9 q^{30}-18 q^{29}+27 q^{28}+31 q^{27}-49 q^{26}-13 q^{25}-59 q^{24}+87 q^{23}+126 q^{22}-73 q^{21}-86 q^{20}-213 q^{19}+140 q^{18}+337 q^{17}+7 q^{16}-163 q^{15}-517 q^{14}+89 q^{13}+591 q^{12}+229 q^{11}-139 q^{10}-875 q^9-102 q^8+759 q^7+506 q^6+4 q^5-1137 q^4-336 q^3+780 q^2+705 q+197-1231 q^{-1} -511 q^{-2} +680 q^{-3} +774 q^{-4} +373 q^{-5} -1163 q^{-6} -603 q^{-7} +492 q^{-8} +734 q^{-9} +523 q^{-10} -959 q^{-11} -626 q^{-12} +241 q^{-13} +596 q^{-14} +626 q^{-15} -637 q^{-16} -564 q^{-17} -32 q^{-18} +366 q^{-19} +632 q^{-20} -282 q^{-21} -396 q^{-22} -210 q^{-23} +107 q^{-24} +494 q^{-25} -25 q^{-26} -169 q^{-27} -221 q^{-28} -68 q^{-29} +275 q^{-30} +61 q^{-31} -8 q^{-32} -123 q^{-33} -101 q^{-34} +102 q^{-35} +39 q^{-36} +35 q^{-37} -37 q^{-38} -57 q^{-39} +25 q^{-40} +8 q^{-41} +20 q^{-42} -4 q^{-43} -18 q^{-44} +4 q^{-45} +5 q^{-47} -3 q^{-49} + q^{-50} </math> \|
	coloured_jones_5 = <math>q^{60}-2 q^{59}+q^{58}+q^{57}-3 q^{56}+q^{55}+5 q^{54}-5 q^{53}+4 q^{51}-10 q^{50}-2 q^{49}+17 q^{48}+2 q^{47}+5 q^{46}-3 q^{45}-39 q^{44}-31 q^{43}+30 q^{42}+67 q^{41}+72 q^{40}+6 q^{39}-146 q^{38}-184 q^{37}-38 q^{36}+191 q^{35}+356 q^{34}+211 q^{33}-251 q^{32}-596 q^{31}-454 q^{30}+155 q^{29}+860 q^{28}+926 q^{27}+16 q^{26}-1104 q^{25}-1429 q^{24}-460 q^{23}+1226 q^{22}+2093 q^{21}+1032 q^{20}-1216 q^{19}-2660 q^{18}-1780 q^{17}+982 q^{16}+3185 q^{15}+2576 q^{14}-607 q^{13}-3544 q^{12}-3325 q^{11}+110 q^{10}+3701 q^9+4010 q^8+425 q^7-3755 q^6-4481 q^5-933 q^4+3609 q^3+4851 q^2+1391 q-3460-4996 q^{-1} -1752 q^{-2} +3163 q^{-3} +5081 q^{-4} +2059 q^{-5} -2903 q^{-6} -4986 q^{-7} -2302 q^{-8} +2518 q^{-9} +4858 q^{-10} +2522 q^{-11} -2125 q^{-12} -4596 q^{-13} -2701 q^{-14} +1618 q^{-15} +4241 q^{-16} +2861 q^{-17} -1051 q^{-18} -3791 q^{-19} -2940 q^{-20} +470 q^{-21} +3153 q^{-22} +2928 q^{-23} +182 q^{-24} -2507 q^{-25} -2764 q^{-26} -662 q^{-27} +1697 q^{-28} +2436 q^{-29} +1124 q^{-30} -1003 q^{-31} -1997 q^{-32} -1260 q^{-33} +304 q^{-34} +1440 q^{-35} +1314 q^{-36} +148 q^{-37} -909 q^{-38} -1096 q^{-39} -465 q^{-40} +425 q^{-41} +855 q^{-42} +538 q^{-43} -89 q^{-44} -531 q^{-45} -512 q^{-46} -112 q^{-47} +297 q^{-48} +378 q^{-49} +176 q^{-50} -101 q^{-51} -251 q^{-52} -177 q^{-53} +17 q^{-54} +141 q^{-55} +120 q^{-56} +28 q^{-57} -59 q^{-58} -84 q^{-59} -33 q^{-60} +29 q^{-61} +42 q^{-62} +18 q^{-63} -2 q^{-64} -18 q^{-65} -20 q^{-66} +4 q^{-67} +11 q^{-68} +3 q^{-69} -5 q^{-72} +3 q^{-74} - q^{-75} </math> \|		coloured_jones_5 = <math>q^{60}-2 q^{59}+q^{58}+q^{57}-3 q^{56}+q^{55}+5 q^{54}-5 q^{53}+4 q^{51}-10 q^{50}-2 q^{49}+17 q^{48}+2 q^{47}+5 q^{46}-3 q^{45}-39 q^{44}-31 q^{43}+30 q^{42}+67 q^{41}+72 q^{40}+6 q^{39}-146 q^{38}-184 q^{37}-38 q^{36}+191 q^{35}+356 q^{34}+211 q^{33}-251 q^{32}-596 q^{31}-454 q^{30}+155 q^{29}+860 q^{28}+926 q^{27}+16 q^{26}-1104 q^{25}-1429 q^{24}-460 q^{23}+1226 q^{22}+2093 q^{21}+1032 q^{20}-1216 q^{19}-2660 q^{18}-1780 q^{17}+982 q^{16}+3185 q^{15}+2576 q^{14}-607 q^{13}-3544 q^{12}-3325 q^{11}+110 q^{10}+3701 q^9+4010 q^8+425 q^7-3755 q^6-4481 q^5-933 q^4+3609 q^3+4851 q^2+1391 q-3460-4996 q^{-1} -1752 q^{-2} +3163 q^{-3} +5081 q^{-4} +2059 q^{-5} -2903 q^{-6} -4986 q^{-7} -2302 q^{-8} +2518 q^{-9} +4858 q^{-10} +2522 q^{-11} -2125 q^{-12} -4596 q^{-13} -2701 q^{-14} +1618 q^{-15} +4241 q^{-16} +2861 q^{-17} -1051 q^{-18} -3791 q^{-19} -2940 q^{-20} +470 q^{-21} +3153 q^{-22} +2928 q^{-23} +182 q^{-24} -2507 q^{-25} -2764 q^{-26} -662 q^{-27} +1697 q^{-28} +2436 q^{-29} +1124 q^{-30} -1003 q^{-31} -1997 q^{-32} -1260 q^{-33} +304 q^{-34} +1440 q^{-35} +1314 q^{-36} +148 q^{-37} -909 q^{-38} -1096 q^{-39} -465 q^{-40} +425 q^{-41} +855 q^{-42} +538 q^{-43} -89 q^{-44} -531 q^{-45} -512 q^{-46} -112 q^{-47} +297 q^{-48} +378 q^{-49} +176 q^{-50} -101 q^{-51} -251 q^{-52} -177 q^{-53} +17 q^{-54} +141 q^{-55} +120 q^{-56} +28 q^{-57} -59 q^{-58} -84 q^{-59} -33 q^{-60} +29 q^{-61} +42 q^{-62} +18 q^{-63} -2 q^{-64} -18 q^{-65} -20 q^{-66} +4 q^{-67} +11 q^{-68} +3 q^{-69} -5 q^{-72} +3 q^{-74} - q^{-75} </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, 37]]</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, 37]]</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[7, 12, 8, 13], X[3, 11, 4, 10], X[11, 3, 12, 2],		<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[7, 12, 8, 13], X[3, 11, 4, 10], X[11, 3, 12, 2],
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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[9, 37]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_37_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, 37]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_37_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, 37]]&) /@ {~~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, 37]]&) /@ {
			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, 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, 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, 37]][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, 37]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:39, 30 August 2005

2005-08-30T14:39:26Z

Show changes

DrorsRobot at 01:07, 30 August 2005

2005-08-30T01:07:01Z

← Older revision		Revision as of 21:07, 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 22:11, 29 August 2005

2005-08-29T22:11:59Z

Show changes

ScottTestRobot at 00:13, 29 August 2005

2005-08-29T00:13:10Z

← Older revision		Revision as of 20:13, 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=9\|k=37\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-5,6,-2,9,-8,3,-4,2,-6,5,-7,8,-9,7/goTop.html}}
	{\| align=left
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=9\|k=37\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-5,6,-2,9,-8,3,-4,2,-6,5,-7,8,-9,7/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>
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	<tr align=center><td>-9</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>-9</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>-11</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>-11</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</nowiki></pre></td></tr>		q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:49, 28 August 2005

2005-08-28T01:49:42Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T21:22:30Z

Resetting knot page to basic template.

New page

9 37 - Revision history

ScottTestRobot at 22:03, 1 September 2005

DrorsRobot at 22:50, 31 August 2005

ScottKnotPageRobot at 14:39, 30 August 2005

DrorsRobot at 01:07, 30 August 2005

DrorsRobot at 22:11, 29 August 2005

ScottTestRobot at 00:13, 29 August 2005

ScottTestRobot at 01:49, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.