ScottTestRobot at 21:57, 1 September 2005

2005-09-01T21:57:31Z

DrorsRobot at 22:40, 31 August 2005

2005-08-31T22:40:53Z

← Older revision		Revision as of 18:40, 31 August 2005
Line 1:		Line 1:
			<!-- WARNING! WARNING! WARNING!
	<!-- This page was generated from the splice template ~~"Rolfsen_Splice_Template"~~. Please do not edit! ~~-->~~		<!-- This page was generated from the splice template [[Rolfsen_Splice_Base]]. Please do not edit!
	<!-- --> <!--
			<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)
	-->
			<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Rolfsen_Splice_Base]]. -->
			<!-- <math>\text{Null}</math> -->
			<!-- <math>\text{Null}</math> -->
	{{Rolfsen Knot Page\|		{{Rolfsen Knot Page\|
	n = 10 \|		n = 10 \|
Line 42:		Line 45:
	coloured_jones_4 = <math>q^{74}-5 q^{73}+5 q^{72}+11 q^{71}-16 q^{70}-6 q^{69}-30 q^{68}+54 q^{67}+103 q^{66}-82 q^{65}-112 q^{64}-251 q^{63}+212 q^{62}+645 q^{61}+48 q^{60}-469 q^{59}-1402 q^{58}-26 q^{57}+2075 q^{56}+1563 q^{55}-206 q^{54}-4248 q^{53}-2542 q^{52}+3229 q^{51}+5529 q^{50}+3239 q^{49}-7254 q^{48}-8631 q^{47}+897 q^{46}+10069 q^{45}+11259 q^{44}-6767 q^{43}-15986 q^{42}-6381 q^{41}+11329 q^{40}+21118 q^{39}-1369 q^{38}-20470 q^{37}-15829 q^{36}+7975 q^{35}+28515 q^{34}+6390 q^{33}-20505 q^{32}-23517 q^{31}+2084 q^{30}+31572 q^{29}+13360 q^{28}-17291 q^{27}-27794 q^{26}-4111 q^{25}+30657 q^{24}+18367 q^{23}-11987 q^{22}-28602 q^{21}-9929 q^{20}+26018 q^{19}+21092 q^{18}-4872 q^{17}-25517 q^{16}-14666 q^{15}+17731 q^{14}+20332 q^{13}+2697 q^{12}-18207 q^{11}-16185 q^{10}+7772 q^9+15153 q^8+7485 q^7-8838 q^6-12951 q^5+302 q^4+7617 q^3+7305 q^2-1746 q-6996-2153 q^{-1} +1895 q^{-2} +4049 q^{-3} +829 q^{-4} -2326 q^{-5} -1348 q^{-6} -201 q^{-7} +1302 q^{-8} +662 q^{-9} -441 q^{-10} -330 q^{-11} -268 q^{-12} +248 q^{-13} +179 q^{-14} -69 q^{-15} -17 q^{-16} -70 q^{-17} +37 q^{-18} +26 q^{-19} -19 q^{-20} +5 q^{-21} -9 q^{-22} +6 q^{-23} +3 q^{-24} -4 q^{-25} + q^{-26} </math> \|		coloured_jones_4 = <math>q^{74}-5 q^{73}+5 q^{72}+11 q^{71}-16 q^{70}-6 q^{69}-30 q^{68}+54 q^{67}+103 q^{66}-82 q^{65}-112 q^{64}-251 q^{63}+212 q^{62}+645 q^{61}+48 q^{60}-469 q^{59}-1402 q^{58}-26 q^{57}+2075 q^{56}+1563 q^{55}-206 q^{54}-4248 q^{53}-2542 q^{52}+3229 q^{51}+5529 q^{50}+3239 q^{49}-7254 q^{48}-8631 q^{47}+897 q^{46}+10069 q^{45}+11259 q^{44}-6767 q^{43}-15986 q^{42}-6381 q^{41}+11329 q^{40}+21118 q^{39}-1369 q^{38}-20470 q^{37}-15829 q^{36}+7975 q^{35}+28515 q^{34}+6390 q^{33}-20505 q^{32}-23517 q^{31}+2084 q^{30}+31572 q^{29}+13360 q^{28}-17291 q^{27}-27794 q^{26}-4111 q^{25}+30657 q^{24}+18367 q^{23}-11987 q^{22}-28602 q^{21}-9929 q^{20}+26018 q^{19}+21092 q^{18}-4872 q^{17}-25517 q^{16}-14666 q^{15}+17731 q^{14}+20332 q^{13}+2697 q^{12}-18207 q^{11}-16185 q^{10}+7772 q^9+15153 q^8+7485 q^7-8838 q^6-12951 q^5+302 q^4+7617 q^3+7305 q^2-1746 q-6996-2153 q^{-1} +1895 q^{-2} +4049 q^{-3} +829 q^{-4} -2326 q^{-5} -1348 q^{-6} -201 q^{-7} +1302 q^{-8} +662 q^{-9} -441 q^{-10} -330 q^{-11} -268 q^{-12} +248 q^{-13} +179 q^{-14} -69 q^{-15} -17 q^{-16} -70 q^{-17} +37 q^{-18} +26 q^{-19} -19 q^{-20} +5 q^{-21} -9 q^{-22} +6 q^{-23} +3 q^{-24} -4 q^{-25} + q^{-26} </math> \|
	coloured_jones_5 = <math>-q^{110}+5 q^{109}-5 q^{108}-11 q^{107}+16 q^{106}+11 q^{105}-10 q^{103}-49 q^{102}-53 q^{101}+77 q^{100}+193 q^{99}+105 q^{98}-147 q^{97}-470 q^{96}-463 q^{95}+146 q^{94}+1142 q^{93}+1425 q^{92}+120 q^{91}-2076 q^{90}-3380 q^{89}-1743 q^{88}+2924 q^{87}+7090 q^{86}+5594 q^{85}-2529 q^{84}-11815 q^{83}-13351 q^{82}-1683 q^{81}+16722 q^{80}+25488 q^{79}+11986 q^{78}-18233 q^{77}-40936 q^{76}-31019 q^{75}+12436 q^{74}+56673 q^{73}+58646 q^{72}+4708 q^{71}-67378 q^{70}-92461 q^{69}-35372 q^{68}+67642 q^{67}+127438 q^{66}+78290 q^{65}-53411 q^{64}-156999 q^{63}-129444 q^{62}+23740 q^{61}+175703 q^{60}+182272 q^{59}+18982 q^{58}-180144 q^{57}-230663 q^{56}-69435 q^{55}+170524 q^{54}+269064 q^{53}+122008 q^{52}-149290 q^{51}-295846 q^{50}-170921 q^{49}+120958 q^{48}+310323 q^{47}+213088 q^{46}-89127 q^{45}-315143 q^{44}-247013 q^{43}+57310 q^{42}+312043 q^{41}+273152 q^{40}-26342 q^{39}-303206 q^{38}-292904 q^{37}-3679 q^{36}+289392 q^{35}+307134 q^{34}+33780 q^{33}-269756 q^{32}-316379 q^{31}-65076 q^{30}+243562 q^{29}+319348 q^{28}+97142 q^{27}-208866 q^{26}-314188 q^{25}-128881 q^{24}+166215 q^{23}+298125 q^{22}+156560 q^{21}-116345 q^{20}-269958 q^{19}-176317 q^{18}+64083 q^{17}+229332 q^{16}+183631 q^{15}-13836 q^{14}-179900 q^{13}-176795 q^{12}-26835 q^{11}+126211 q^{10}+155697 q^9+54716 q^8-75683 q^7-124947 q^6-66442 q^5+33970 q^4+89488 q^3+64870 q^2-5068 q-56439-53407 q^{-1} -10729 q^{-2} +29891 q^{-3} +38155 q^{-4} +15804 q^{-5} -12198 q^{-6} -23416 q^{-7} -14367 q^{-8} +2521 q^{-9} +12382 q^{-10} +10079 q^{-11} +1302 q^{-12} -5328 q^{-13} -5903 q^{-14} -2040 q^{-15} +1877 q^{-16} +2885 q^{-17} +1431 q^{-18} -405 q^{-19} -1165 q^{-20} -799 q^{-21} -6 q^{-22} +435 q^{-23} +328 q^{-24} +26 q^{-25} -111 q^{-26} -98 q^{-27} -46 q^{-28} +40 q^{-29} +47 q^{-30} -15 q^{-31} -9 q^{-32} +6 q^{-33} -6 q^{-34} +9 q^{-36} -6 q^{-37} -3 q^{-38} +4 q^{-39} - q^{-40} </math> \|		coloured_jones_5 = <math>-q^{110}+5 q^{109}-5 q^{108}-11 q^{107}+16 q^{106}+11 q^{105}-10 q^{103}-49 q^{102}-53 q^{101}+77 q^{100}+193 q^{99}+105 q^{98}-147 q^{97}-470 q^{96}-463 q^{95}+146 q^{94}+1142 q^{93}+1425 q^{92}+120 q^{91}-2076 q^{90}-3380 q^{89}-1743 q^{88}+2924 q^{87}+7090 q^{86}+5594 q^{85}-2529 q^{84}-11815 q^{83}-13351 q^{82}-1683 q^{81}+16722 q^{80}+25488 q^{79}+11986 q^{78}-18233 q^{77}-40936 q^{76}-31019 q^{75}+12436 q^{74}+56673 q^{73}+58646 q^{72}+4708 q^{71}-67378 q^{70}-92461 q^{69}-35372 q^{68}+67642 q^{67}+127438 q^{66}+78290 q^{65}-53411 q^{64}-156999 q^{63}-129444 q^{62}+23740 q^{61}+175703 q^{60}+182272 q^{59}+18982 q^{58}-180144 q^{57}-230663 q^{56}-69435 q^{55}+170524 q^{54}+269064 q^{53}+122008 q^{52}-149290 q^{51}-295846 q^{50}-170921 q^{49}+120958 q^{48}+310323 q^{47}+213088 q^{46}-89127 q^{45}-315143 q^{44}-247013 q^{43}+57310 q^{42}+312043 q^{41}+273152 q^{40}-26342 q^{39}-303206 q^{38}-292904 q^{37}-3679 q^{36}+289392 q^{35}+307134 q^{34}+33780 q^{33}-269756 q^{32}-316379 q^{31}-65076 q^{30}+243562 q^{29}+319348 q^{28}+97142 q^{27}-208866 q^{26}-314188 q^{25}-128881 q^{24}+166215 q^{23}+298125 q^{22}+156560 q^{21}-116345 q^{20}-269958 q^{19}-176317 q^{18}+64083 q^{17}+229332 q^{16}+183631 q^{15}-13836 q^{14}-179900 q^{13}-176795 q^{12}-26835 q^{11}+126211 q^{10}+155697 q^9+54716 q^8-75683 q^7-124947 q^6-66442 q^5+33970 q^4+89488 q^3+64870 q^2-5068 q-56439-53407 q^{-1} -10729 q^{-2} +29891 q^{-3} +38155 q^{-4} +15804 q^{-5} -12198 q^{-6} -23416 q^{-7} -14367 q^{-8} +2521 q^{-9} +12382 q^{-10} +10079 q^{-11} +1302 q^{-12} -5328 q^{-13} -5903 q^{-14} -2040 q^{-15} +1877 q^{-16} +2885 q^{-17} +1431 q^{-18} -405 q^{-19} -1165 q^{-20} -799 q^{-21} -6 q^{-22} +435 q^{-23} +328 q^{-24} +26 q^{-25} -111 q^{-26} -98 q^{-27} -46 q^{-28} +40 q^{-29} +47 q^{-30} -15 q^{-31} -9 q^{-32} +6 q^{-33} -6 q^{-34} +9 q^{-36} -6 q^{-37} -3 q^{-38} +4 q^{-39} - q^{-40} </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>
Line 50:		Line 53:
	<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, 113]]</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, 113]]</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, 4, 11, 3], X[14, 6, 15, 5], X[20, 16, 1, 15],		<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, 4, 11, 3], X[14, 6, 15, 5], X[20, 16, 1, 15],
Line 70:		Line 73:
	<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>4</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>4</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, 113]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_113_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, 113]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_113_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, 113]]&) /@ {~~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, 113]]&) /@ {
			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, 113]][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, 113]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:33, 30 August 2005

2005-08-30T14:33:30Z

Show changes

DrorsRobot at 01:00, 30 August 2005

2005-08-30T01:00:17Z

← Older revision		Revision as of 21:00, 29 August 2005
Line 1:		Line 1:
			<!-- This page was generated from the splice template "Rolfsen_Splice_Template". Please do not edit! -->
	<!-- -->		<!-- -->
	<!-- -->		<!-- -->
Line 217:		Line 218:
	</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 21:58, 29 August 2005

2005-08-29T21:58:36Z

Show changes

ScottTestRobot at 00:05, 29 August 2005

2005-08-29T00:05:49Z

← Older revision		Revision as of 20:05, 28 August 2005
Line 1:		Line 1:
	<!-- -->		<!-- -->
			<!-- -->

			<!-- -->
			<!-- -->
	<!-- 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=113\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,3,-7,5,-6,10,-2,8,-5,9,-3,4,-8,6,-9,7,-4/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=113\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,3,-7,5,-6,10,-2,8,-5,9,-3,4,-8,6,-9,7,-4/goTop.html}}
	\|{{:{{PAGENAME}} Quick Notes}}
	\|}

	<br style="clear:both" />		<br style="clear:both" />
Line 24:		Line 21:
	{{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>
Line 48:		Line 41:
	<tr align=center><td>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>3</td></tr>		<tr align=center><td>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>3</td></tr>
	<tr align=center><td>-5</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>-5</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}}

Line 143:		Line 135:
	4 q t + 6 q t + q t + 4 q t + q t</nowiki></pre></td></tr>		4 q t + 6 q t + q t + 4 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:44, 28 August 2005

2005-08-28T01:44:39Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:00Z

Resetting knot page to basic template.

New page

10 113 - Revision history

ScottTestRobot at 21:57, 1 September 2005

DrorsRobot at 22:40, 31 August 2005

ScottKnotPageRobot at 14:33, 30 August 2005

DrorsRobot at 01:00, 30 August 2005

DrorsRobot at 21:58, 29 August 2005

ScottTestRobot at 00:05, 29 August 2005

ScottTestRobot at 01:44, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.