ScottTestRobot at 22:05, 1 September 2005

2005-09-01T22:05:04Z

DrorsRobot at 22:53, 31 August 2005

2005-08-31T22:53:30Z

← Older revision		Revision as of 18:53, 31 August 2005
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	coloured_jones_4 = <math>q^{74}-3 q^{73}+q^{72}+5 q^{71}-3 q^{70}+2 q^{69}-19 q^{68}+4 q^{67}+35 q^{66}+5 q^{65}+6 q^{64}-100 q^{63}-38 q^{62}+108 q^{61}+105 q^{60}+116 q^{59}-260 q^{58}-268 q^{57}+55 q^{56}+286 q^{55}+546 q^{54}-254 q^{53}-651 q^{52}-380 q^{51}+228 q^{50}+1217 q^{49}+209 q^{48}-799 q^{47}-1105 q^{46}-348 q^{45}+1710 q^{44}+1002 q^{43}-452 q^{42}-1713 q^{41}-1256 q^{40}+1765 q^{39}+1727 q^{38}+220 q^{37}-1981 q^{36}-2105 q^{35}+1508 q^{34}+2169 q^{33}+889 q^{32}-1969 q^{31}-2683 q^{30}+1123 q^{29}+2332 q^{28}+1419 q^{27}-1747 q^{26}-2957 q^{25}+634 q^{24}+2205 q^{23}+1798 q^{22}-1260 q^{21}-2863 q^{20}+26 q^{19}+1701 q^{18}+1925 q^{17}-533 q^{16}-2296 q^{15}-489 q^{14}+881 q^{13}+1614 q^{12}+137 q^{11}-1364 q^{10}-612 q^9+132 q^8+950 q^7+384 q^6-521 q^5-358 q^4-174 q^3+345 q^2+250 q-109-89 q^{-1} -128 q^{-2} +72 q^{-3} +77 q^{-4} -20 q^{-5} +3 q^{-6} -38 q^{-7} +12 q^{-8} +14 q^{-9} -9 q^{-10} +5 q^{-11} -6 q^{-12} +3 q^{-13} +2 q^{-14} -3 q^{-15} + q^{-16} </math> \|		coloured_jones_4 = <math>q^{74}-3 q^{73}+q^{72}+5 q^{71}-3 q^{70}+2 q^{69}-19 q^{68}+4 q^{67}+35 q^{66}+5 q^{65}+6 q^{64}-100 q^{63}-38 q^{62}+108 q^{61}+105 q^{60}+116 q^{59}-260 q^{58}-268 q^{57}+55 q^{56}+286 q^{55}+546 q^{54}-254 q^{53}-651 q^{52}-380 q^{51}+228 q^{50}+1217 q^{49}+209 q^{48}-799 q^{47}-1105 q^{46}-348 q^{45}+1710 q^{44}+1002 q^{43}-452 q^{42}-1713 q^{41}-1256 q^{40}+1765 q^{39}+1727 q^{38}+220 q^{37}-1981 q^{36}-2105 q^{35}+1508 q^{34}+2169 q^{33}+889 q^{32}-1969 q^{31}-2683 q^{30}+1123 q^{29}+2332 q^{28}+1419 q^{27}-1747 q^{26}-2957 q^{25}+634 q^{24}+2205 q^{23}+1798 q^{22}-1260 q^{21}-2863 q^{20}+26 q^{19}+1701 q^{18}+1925 q^{17}-533 q^{16}-2296 q^{15}-489 q^{14}+881 q^{13}+1614 q^{12}+137 q^{11}-1364 q^{10}-612 q^9+132 q^8+950 q^7+384 q^6-521 q^5-358 q^4-174 q^3+345 q^2+250 q-109-89 q^{-1} -128 q^{-2} +72 q^{-3} +77 q^{-4} -20 q^{-5} +3 q^{-6} -38 q^{-7} +12 q^{-8} +14 q^{-9} -9 q^{-10} +5 q^{-11} -6 q^{-12} +3 q^{-13} +2 q^{-14} -3 q^{-15} + q^{-16} </math> \|
	coloured_jones_5 = <math>-q^{110}+3 q^{109}-q^{108}-5 q^{107}+3 q^{106}+3 q^{105}+q^{104}+7 q^{103}-6 q^{102}-30 q^{101}-8 q^{100}+29 q^{99}+47 q^{98}+52 q^{97}-20 q^{96}-132 q^{95}-159 q^{94}-11 q^{93}+211 q^{92}+349 q^{91}+212 q^{90}-236 q^{89}-649 q^{88}-610 q^{87}+50 q^{86}+918 q^{85}+1245 q^{84}+513 q^{83}-945 q^{82}-2007 q^{81}-1554 q^{80}+511 q^{79}+2637 q^{78}+2919 q^{77}+657 q^{76}-2779 q^{75}-4485 q^{74}-2468 q^{73}+2201 q^{72}+5738 q^{71}+4783 q^{70}-680 q^{69}-6469 q^{68}-7254 q^{67}-1549 q^{66}+6351 q^{65}+9482 q^{64}+4321 q^{63}-5428 q^{62}-11228 q^{61}-7211 q^{60}+3854 q^{59}+12318 q^{58}+9944 q^{57}-1903 q^{56}-12793 q^{55}-12309 q^{54}-134 q^{53}+12791 q^{52}+14176 q^{51}+2110 q^{50}-12498 q^{49}-15624 q^{48}-3802 q^{47}+11986 q^{46}+16645 q^{45}+5371 q^{44}-11403 q^{43}-17433 q^{42}-6638 q^{41}+10627 q^{40}+17843 q^{39}+7990 q^{38}-9684 q^{37}-18085 q^{36}-9117 q^{35}+8360 q^{34}+17780 q^{33}+10381 q^{32}-6663 q^{31}-17086 q^{30}-11311 q^{29}+4551 q^{28}+15589 q^{27}+12021 q^{26}-2183 q^{25}-13495 q^{24}-12040 q^{23}-208 q^{22}+10743 q^{21}+11390 q^{20}+2243 q^{19}-7720 q^{18}-9909 q^{17}-3653 q^{16}+4709 q^{15}+7949 q^{14}+4195 q^{13}-2223 q^{12}-5645 q^{11}-3988 q^{10}+414 q^9+3563 q^8+3232 q^7+517 q^6-1862 q^5-2242 q^4-849 q^3+768 q^2+1346 q+749-192 q^{-1} -679 q^{-2} -506 q^{-3} -28 q^{-4} +280 q^{-5} +281 q^{-6} +78 q^{-7} -109 q^{-8} -129 q^{-9} -39 q^{-10} +25 q^{-11} +41 q^{-12} +35 q^{-13} -11 q^{-14} -25 q^{-15} +2 q^{-16} +3 q^{-17} -3 q^{-18} +6 q^{-19} + q^{-20} -6 q^{-21} +3 q^{-22} +2 q^{-23} -3 q^{-24} + q^{-25} </math> \|		coloured_jones_5 = <math>-q^{110}+3 q^{109}-q^{108}-5 q^{107}+3 q^{106}+3 q^{105}+q^{104}+7 q^{103}-6 q^{102}-30 q^{101}-8 q^{100}+29 q^{99}+47 q^{98}+52 q^{97}-20 q^{96}-132 q^{95}-159 q^{94}-11 q^{93}+211 q^{92}+349 q^{91}+212 q^{90}-236 q^{89}-649 q^{88}-610 q^{87}+50 q^{86}+918 q^{85}+1245 q^{84}+513 q^{83}-945 q^{82}-2007 q^{81}-1554 q^{80}+511 q^{79}+2637 q^{78}+2919 q^{77}+657 q^{76}-2779 q^{75}-4485 q^{74}-2468 q^{73}+2201 q^{72}+5738 q^{71}+4783 q^{70}-680 q^{69}-6469 q^{68}-7254 q^{67}-1549 q^{66}+6351 q^{65}+9482 q^{64}+4321 q^{63}-5428 q^{62}-11228 q^{61}-7211 q^{60}+3854 q^{59}+12318 q^{58}+9944 q^{57}-1903 q^{56}-12793 q^{55}-12309 q^{54}-134 q^{53}+12791 q^{52}+14176 q^{51}+2110 q^{50}-12498 q^{49}-15624 q^{48}-3802 q^{47}+11986 q^{46}+16645 q^{45}+5371 q^{44}-11403 q^{43}-17433 q^{42}-6638 q^{41}+10627 q^{40}+17843 q^{39}+7990 q^{38}-9684 q^{37}-18085 q^{36}-9117 q^{35}+8360 q^{34}+17780 q^{33}+10381 q^{32}-6663 q^{31}-17086 q^{30}-11311 q^{29}+4551 q^{28}+15589 q^{27}+12021 q^{26}-2183 q^{25}-13495 q^{24}-12040 q^{23}-208 q^{22}+10743 q^{21}+11390 q^{20}+2243 q^{19}-7720 q^{18}-9909 q^{17}-3653 q^{16}+4709 q^{15}+7949 q^{14}+4195 q^{13}-2223 q^{12}-5645 q^{11}-3988 q^{10}+414 q^9+3563 q^8+3232 q^7+517 q^6-1862 q^5-2242 q^4-849 q^3+768 q^2+1346 q+749-192 q^{-1} -679 q^{-2} -506 q^{-3} -28 q^{-4} +280 q^{-5} +281 q^{-6} +78 q^{-7} -109 q^{-8} -129 q^{-9} -39 q^{-10} +25 q^{-11} +41 q^{-12} +35 q^{-13} -11 q^{-14} -25 q^{-15} +2 q^{-16} +3 q^{-17} -3 q^{-18} +6 q^{-19} + q^{-20} -6 q^{-21} +3 q^{-22} +2 q^{-23} -3 q^{-24} + q^{-25} </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, 39]]</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, 39]]</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, 11, 4, 10], X[7, 18, 8, 1], X[17, 13, 18, 12],		<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, 11, 4, 10], X[7, 18, 8, 1], X[17, 13, 18, 12],
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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, 39]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_39_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, 39]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_39_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, 39]]&) /@ {~~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, 39]]&) /@ {
			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, 2, 3, {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, 1, 2, 3, {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, 39]][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, 39]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:41, 30 August 2005

2005-08-30T14:41:06Z

Show changes

DrorsRobot at 01:08, 30 August 2005

2005-08-30T01:08:59Z

← Older revision		Revision as of 21:08, 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 22:12, 29 August 2005

2005-08-29T22:12:14Z

Show changes

ScottTestRobot at 00:15, 29 August 2005

2005-08-29T00:15:21Z

← Older revision		Revision as of 20:15, 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=39\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,8,-2,7,-6,1,-3,9,-5,2,-8,4,-9,6,-7,5,-4,3/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=9\|k=39\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,8,-2,7,-6,1,-3,9,-5,2,-8,4,-9,6,-7,5,-4,3/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=14.2857%><table cellpadding=0 cellspacing=0>		<td width=14.2857%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>-1</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>-1</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>-3</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>-3</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 + 2 q t + q t</nowiki></pre></td></tr>		q t + 2 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:51, 28 August 2005

2005-08-28T01:51:42Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T21:22:32Z

Resetting knot page to basic template.

New page

9 39 - Revision history

ScottTestRobot at 22:05, 1 September 2005

DrorsRobot at 22:53, 31 August 2005

ScottKnotPageRobot at 14:41, 30 August 2005

DrorsRobot at 01:08, 30 August 2005

DrorsRobot at 22:12, 29 August 2005

ScottTestRobot at 00:15, 29 August 2005

ScottTestRobot at 01:51, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.