ScottTestRobot at 21:57, 1 September 2005

2005-09-01T21:57:07Z

DrorsRobot at 22:40, 31 August 2005

2005-08-31T22:40:21Z

← 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}-3 q^{73}+2 q^{72}+4 q^{71}-6 q^{70}+3 q^{69}-15 q^{68}+14 q^{67}+32 q^{66}-24 q^{65}-9 q^{64}-86 q^{63}+40 q^{62}+165 q^{61}+7 q^{60}-41 q^{59}-367 q^{58}-42 q^{57}+457 q^{56}+306 q^{55}+117 q^{54}-972 q^{53}-571 q^{52}+672 q^{51}+1024 q^{50}+906 q^{49}-1618 q^{48}-1741 q^{47}+273 q^{46}+1854 q^{45}+2550 q^{44}-1717 q^{43}-3213 q^{42}-992 q^{41}+2220 q^{40}+4630 q^{39}-998 q^{38}-4334 q^{37}-2753 q^{36}+1857 q^{35}+6434 q^{34}+235 q^{33}-4745 q^{32}-4371 q^{31}+981 q^{30}+7489 q^{29}+1508 q^{28}-4466 q^{27}-5445 q^{26}-101 q^{25}+7652 q^{24}+2556 q^{23}-3597 q^{22}-5814 q^{21}-1235 q^{20}+6865 q^{19}+3243 q^{18}-2210 q^{17}-5366 q^{16}-2232 q^{15}+5199 q^{14}+3327 q^{13}-620 q^{12}-4081 q^{11}-2700 q^{10}+3081 q^9+2656 q^8+573 q^7-2366 q^6-2372 q^5+1288 q^4+1535 q^3+941 q^2-934 q-1509+320 q^{-1} +575 q^{-2} +686 q^{-3} -196 q^{-4} -697 q^{-5} +35 q^{-6} +102 q^{-7} +316 q^{-8} +9 q^{-9} -243 q^{-10} +10 q^{-11} -14 q^{-12} +102 q^{-13} +18 q^{-14} -70 q^{-15} +12 q^{-16} -13 q^{-17} +24 q^{-18} +6 q^{-19} -17 q^{-20} +5 q^{-21} -3 q^{-22} +4 q^{-23} + q^{-24} -3 q^{-25} + q^{-26} </math> \|		coloured_jones_4 = <math>q^{74}-3 q^{73}+2 q^{72}+4 q^{71}-6 q^{70}+3 q^{69}-15 q^{68}+14 q^{67}+32 q^{66}-24 q^{65}-9 q^{64}-86 q^{63}+40 q^{62}+165 q^{61}+7 q^{60}-41 q^{59}-367 q^{58}-42 q^{57}+457 q^{56}+306 q^{55}+117 q^{54}-972 q^{53}-571 q^{52}+672 q^{51}+1024 q^{50}+906 q^{49}-1618 q^{48}-1741 q^{47}+273 q^{46}+1854 q^{45}+2550 q^{44}-1717 q^{43}-3213 q^{42}-992 q^{41}+2220 q^{40}+4630 q^{39}-998 q^{38}-4334 q^{37}-2753 q^{36}+1857 q^{35}+6434 q^{34}+235 q^{33}-4745 q^{32}-4371 q^{31}+981 q^{30}+7489 q^{29}+1508 q^{28}-4466 q^{27}-5445 q^{26}-101 q^{25}+7652 q^{24}+2556 q^{23}-3597 q^{22}-5814 q^{21}-1235 q^{20}+6865 q^{19}+3243 q^{18}-2210 q^{17}-5366 q^{16}-2232 q^{15}+5199 q^{14}+3327 q^{13}-620 q^{12}-4081 q^{11}-2700 q^{10}+3081 q^9+2656 q^8+573 q^7-2366 q^6-2372 q^5+1288 q^4+1535 q^3+941 q^2-934 q-1509+320 q^{-1} +575 q^{-2} +686 q^{-3} -196 q^{-4} -697 q^{-5} +35 q^{-6} +102 q^{-7} +316 q^{-8} +9 q^{-9} -243 q^{-10} +10 q^{-11} -14 q^{-12} +102 q^{-13} +18 q^{-14} -70 q^{-15} +12 q^{-16} -13 q^{-17} +24 q^{-18} +6 q^{-19} -17 q^{-20} +5 q^{-21} -3 q^{-22} +4 q^{-23} + q^{-24} -3 q^{-25} + q^{-26} </math> \|
	coloured_jones_5 = <math>-q^{110}+3 q^{109}-2 q^{108}-4 q^{107}+6 q^{106}+2 q^{105}-4 q^{104}+4 q^{103}-9 q^{102}-20 q^{101}+18 q^{100}+39 q^{99}+12 q^{98}-5 q^{97}-72 q^{96}-107 q^{95}+q^{94}+177 q^{93}+233 q^{92}+88 q^{91}-253 q^{90}-550 q^{89}-355 q^{88}+315 q^{87}+985 q^{86}+953 q^{85}-130 q^{84}-1563 q^{83}-1956 q^{82}-529 q^{81}+1978 q^{80}+3504 q^{79}+1967 q^{78}-2082 q^{77}-5264 q^{76}-4325 q^{75}+1138 q^{74}+7133 q^{73}+7721 q^{72}+868 q^{71}-8382 q^{70}-11715 q^{69}-4551 q^{68}+8635 q^{67}+16102 q^{66}+9450 q^{65}-7391 q^{64}-20027 q^{63}-15524 q^{62}+4559 q^{61}+23142 q^{60}+22010 q^{59}-280 q^{58}-24937 q^{57}-28407 q^{56}-5039 q^{55}+25357 q^{54}+34133 q^{53}+10867 q^{52}-24534 q^{51}-38763 q^{50}-16734 q^{49}+22677 q^{48}+42328 q^{47}+22081 q^{46}-20190 q^{45}-44518 q^{44}-26909 q^{43}+17195 q^{42}+45882 q^{41}+30809 q^{40}-14055 q^{39}-45895 q^{38}-34176 q^{37}+10486 q^{36}+45346 q^{35}+36615 q^{34}-6845 q^{33}-43341 q^{32}-38528 q^{31}+2651 q^{30}+40641 q^{29}+39418 q^{28}+1558 q^{27}-36357 q^{26}-39401 q^{25}-6048 q^{24}+31277 q^{23}+37958 q^{22}+10054 q^{21}-24954 q^{20}-35247 q^{19}-13438 q^{18}+18417 q^{17}+31021 q^{16}+15490 q^{15}-11689 q^{14}-25873 q^{13}-16211 q^{12}+5995 q^{11}+20010 q^{10}+15330 q^9-1317 q^8-14308 q^7-13391 q^6-1630 q^5+9231 q^4+10599 q^3+3223 q^2-5233 q-7728-3548 q^{-1} +2461 q^{-2} +5105 q^{-3} +3120 q^{-4} -790 q^{-5} -3052 q^{-6} -2356 q^{-7} -38 q^{-8} +1651 q^{-9} +1565 q^{-10} +312 q^{-11} -786 q^{-12} -933 q^{-13} -315 q^{-14} +326 q^{-15} +498 q^{-16} +234 q^{-17} -120 q^{-18} -256 q^{-19} -119 q^{-20} +39 q^{-21} +96 q^{-22} +76 q^{-23} -7 q^{-24} -62 q^{-25} -21 q^{-26} +15 q^{-27} +5 q^{-28} +14 q^{-29} +6 q^{-30} -19 q^{-31} -2 q^{-32} +9 q^{-33} -2 q^{-34} +3 q^{-36} -4 q^{-37} - q^{-38} +3 q^{-39} - q^{-40} </math> \|		coloured_jones_5 = <math>-q^{110}+3 q^{109}-2 q^{108}-4 q^{107}+6 q^{106}+2 q^{105}-4 q^{104}+4 q^{103}-9 q^{102}-20 q^{101}+18 q^{100}+39 q^{99}+12 q^{98}-5 q^{97}-72 q^{96}-107 q^{95}+q^{94}+177 q^{93}+233 q^{92}+88 q^{91}-253 q^{90}-550 q^{89}-355 q^{88}+315 q^{87}+985 q^{86}+953 q^{85}-130 q^{84}-1563 q^{83}-1956 q^{82}-529 q^{81}+1978 q^{80}+3504 q^{79}+1967 q^{78}-2082 q^{77}-5264 q^{76}-4325 q^{75}+1138 q^{74}+7133 q^{73}+7721 q^{72}+868 q^{71}-8382 q^{70}-11715 q^{69}-4551 q^{68}+8635 q^{67}+16102 q^{66}+9450 q^{65}-7391 q^{64}-20027 q^{63}-15524 q^{62}+4559 q^{61}+23142 q^{60}+22010 q^{59}-280 q^{58}-24937 q^{57}-28407 q^{56}-5039 q^{55}+25357 q^{54}+34133 q^{53}+10867 q^{52}-24534 q^{51}-38763 q^{50}-16734 q^{49}+22677 q^{48}+42328 q^{47}+22081 q^{46}-20190 q^{45}-44518 q^{44}-26909 q^{43}+17195 q^{42}+45882 q^{41}+30809 q^{40}-14055 q^{39}-45895 q^{38}-34176 q^{37}+10486 q^{36}+45346 q^{35}+36615 q^{34}-6845 q^{33}-43341 q^{32}-38528 q^{31}+2651 q^{30}+40641 q^{29}+39418 q^{28}+1558 q^{27}-36357 q^{26}-39401 q^{25}-6048 q^{24}+31277 q^{23}+37958 q^{22}+10054 q^{21}-24954 q^{20}-35247 q^{19}-13438 q^{18}+18417 q^{17}+31021 q^{16}+15490 q^{15}-11689 q^{14}-25873 q^{13}-16211 q^{12}+5995 q^{11}+20010 q^{10}+15330 q^9-1317 q^8-14308 q^7-13391 q^6-1630 q^5+9231 q^4+10599 q^3+3223 q^2-5233 q-7728-3548 q^{-1} +2461 q^{-2} +5105 q^{-3} +3120 q^{-4} -790 q^{-5} -3052 q^{-6} -2356 q^{-7} -38 q^{-8} +1651 q^{-9} +1565 q^{-10} +312 q^{-11} -786 q^{-12} -933 q^{-13} -315 q^{-14} +326 q^{-15} +498 q^{-16} +234 q^{-17} -120 q^{-18} -256 q^{-19} -119 q^{-20} +39 q^{-21} +96 q^{-22} +76 q^{-23} -7 q^{-24} -62 q^{-25} -21 q^{-26} +15 q^{-27} +5 q^{-28} +14 q^{-29} +6 q^{-30} -19 q^{-31} -2 q^{-32} +9 q^{-33} -2 q^{-34} +3 q^{-36} -4 q^{-37} - q^{-38} +3 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, 57]]</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, 57]]</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[3, 8, 4, 9], X[9, 15, 10, 14], X[5, 13, 6, 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, 4, 2, 5], X[3, 8, 4, 9], X[9, 15, 10, 14], X[5, 13, 6, 12],
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, 57]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_57_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, 57]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_57_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, 57]]&) /@ {~~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, 57]]&) /@ {
			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, 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, 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, 57]][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, 57]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:33, 30 August 2005

2005-08-30T14:33:08Z

Show changes

DrorsRobot at 00:59, 30 August 2005

2005-08-30T00:59:51Z

← Older revision		Revision as of 20:59, 29 August 2005
Line 1:		Line 1:
			<!-- This page was generated from the splice template "Rolfsen_Splice_Template". Please do not edit! -->
	<!-- -->		<!-- -->
	<!-- -->		<!-- -->
Line 223:		Line 224:
	</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 21:57, 29 August 2005

2005-08-29T21:57:44Z

Show changes

ScottTestRobot at 00:05, 29 August 2005

2005-08-29T00:05:29Z

← 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=57\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,5,-10,2,-3,9,-6,4,-5,3,-7,8,-9,6,-8,7/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=57\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,5,-10,2,-3,9,-6,4,-5,3,-7,8,-9,6,-8,7/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>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>-3</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>-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:
	2 q t + 5 q t + q t + 2 q t + q t</nowiki></pre></td></tr>		2 q t + 5 q t + q t + 2 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:44, 28 August 2005

2005-08-28T01:44:24Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:09Z

Resetting knot page to basic template.

New page

10 57 - 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 00:59, 30 August 2005

DrorsRobot at 21:57, 29 August 2005

ScottTestRobot at 00:05, 29 August 2005

ScottTestRobot at 01:44, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.