ScottTestRobot at 22:02, 1 September 2005

2005-09-01T22:02:23Z

DrorsRobot at 22:48, 31 August 2005

2005-08-31T22:48:12Z

← Older revision		Revision as of 18:48, 31 August 2005
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	coloured_jones_4 = <math>q^{60}-4 q^{59}+q^{58}+9 q^{57}-q^{56}+2 q^{55}-35 q^{54}-10 q^{53}+50 q^{52}+38 q^{51}+59 q^{50}-142 q^{49}-149 q^{48}+41 q^{47}+156 q^{46}+391 q^{45}-146 q^{44}-466 q^{43}-343 q^{42}+20 q^{41}+1047 q^{40}+406 q^{39}-470 q^{38}-1099 q^{37}-948 q^{36}+1348 q^{35}+1450 q^{34}+544 q^{33}-1411 q^{32}-2611 q^{31}+512 q^{30}+2056 q^{29}+2401 q^{28}-500 q^{27}-3959 q^{26}-1275 q^{25}+1478 q^{24}+4126 q^{23}+1389 q^{22}-4268 q^{21}-3117 q^{20}-28 q^{19}+5059 q^{18}+3417 q^{17}-3695 q^{16}-4449 q^{15}-1756 q^{14}+5267 q^{13}+5060 q^{12}-2692 q^{11}-5219 q^{10}-3322 q^9+4901 q^8+6185 q^7-1368 q^6-5337 q^5-4613 q^4+3810 q^3+6521 q^2+234 q-4448-5236 q^{-1} +1987 q^{-2} +5610 q^{-3} +1575 q^{-4} -2600 q^{-5} -4632 q^{-6} +189 q^{-7} +3592 q^{-8} +1882 q^{-9} -709 q^{-10} -2969 q^{-11} -655 q^{-12} +1544 q^{-13} +1209 q^{-14} +251 q^{-15} -1302 q^{-16} -537 q^{-17} +396 q^{-18} +411 q^{-19} +326 q^{-20} -385 q^{-21} -188 q^{-22} +60 q^{-23} +37 q^{-24} +145 q^{-25} -88 q^{-26} -22 q^{-27} +16 q^{-28} -29 q^{-29} +40 q^{-30} -20 q^{-31} +5 q^{-32} +8 q^{-33} -14 q^{-34} +8 q^{-35} -4 q^{-36} +2 q^{-37} +2 q^{-38} -3 q^{-39} + q^{-40} </math> \|		coloured_jones_4 = <math>q^{60}-4 q^{59}+q^{58}+9 q^{57}-q^{56}+2 q^{55}-35 q^{54}-10 q^{53}+50 q^{52}+38 q^{51}+59 q^{50}-142 q^{49}-149 q^{48}+41 q^{47}+156 q^{46}+391 q^{45}-146 q^{44}-466 q^{43}-343 q^{42}+20 q^{41}+1047 q^{40}+406 q^{39}-470 q^{38}-1099 q^{37}-948 q^{36}+1348 q^{35}+1450 q^{34}+544 q^{33}-1411 q^{32}-2611 q^{31}+512 q^{30}+2056 q^{29}+2401 q^{28}-500 q^{27}-3959 q^{26}-1275 q^{25}+1478 q^{24}+4126 q^{23}+1389 q^{22}-4268 q^{21}-3117 q^{20}-28 q^{19}+5059 q^{18}+3417 q^{17}-3695 q^{16}-4449 q^{15}-1756 q^{14}+5267 q^{13}+5060 q^{12}-2692 q^{11}-5219 q^{10}-3322 q^9+4901 q^8+6185 q^7-1368 q^6-5337 q^5-4613 q^4+3810 q^3+6521 q^2+234 q-4448-5236 q^{-1} +1987 q^{-2} +5610 q^{-3} +1575 q^{-4} -2600 q^{-5} -4632 q^{-6} +189 q^{-7} +3592 q^{-8} +1882 q^{-9} -709 q^{-10} -2969 q^{-11} -655 q^{-12} +1544 q^{-13} +1209 q^{-14} +251 q^{-15} -1302 q^{-16} -537 q^{-17} +396 q^{-18} +411 q^{-19} +326 q^{-20} -385 q^{-21} -188 q^{-22} +60 q^{-23} +37 q^{-24} +145 q^{-25} -88 q^{-26} -22 q^{-27} +16 q^{-28} -29 q^{-29} +40 q^{-30} -20 q^{-31} +5 q^{-32} +8 q^{-33} -14 q^{-34} +8 q^{-35} -4 q^{-36} +2 q^{-37} +2 q^{-38} -3 q^{-39} + q^{-40} </math> \|
	coloured_jones_5 = <math>q^{90}-4 q^{89}+q^{88}+9 q^{87}-q^{86}-4 q^{85}-10 q^{84}-20 q^{83}-3 q^{82}+53 q^{81}+57 q^{80}+9 q^{79}-65 q^{78}-151 q^{77}-129 q^{76}+63 q^{75}+320 q^{74}+351 q^{73}+81 q^{72}-395 q^{71}-767 q^{70}-571 q^{69}+300 q^{68}+1236 q^{67}+1361 q^{66}+362 q^{65}-1364 q^{64}-2524 q^{63}-1744 q^{62}+845 q^{61}+3444 q^{60}+3784 q^{59}+944 q^{58}-3570 q^{57}-6123 q^{56}-3944 q^{55}+2142 q^{54}+7801 q^{53}+7945 q^{52}+1232 q^{51}-7936 q^{50}-12002 q^{49}-6459 q^{48}+5733 q^{47}+15075 q^{46}+12790 q^{45}-987 q^{44}-16028 q^{43}-19243 q^{42}-5945 q^{41}+14406 q^{40}+24602 q^{39}+14131 q^{38}-10120 q^{37}-28002 q^{36}-22616 q^{35}+3740 q^{34}+29233 q^{33}+30312 q^{32}+3785 q^{31}-28199 q^{30}-36688 q^{29}-11811 q^{28}+25764 q^{27}+41502 q^{26}+19260 q^{25}-22173 q^{24}-44870 q^{23}-26171 q^{22}+18380 q^{21}+47190 q^{20}+31969 q^{19}-14339 q^{18}-48648 q^{17}-37297 q^{16}+10504 q^{15}+49507 q^{14}+41817 q^{13}-6259 q^{12}-49591 q^{11}-46135 q^{10}+1776 q^9+48605 q^8+49590 q^7+3628 q^6-46021 q^5-52288 q^4-9434 q^3+41535 q^2+53054 q+15615-34918 q^{-1} -51744 q^{-2} -21076 q^{-3} +26730 q^{-4} +47626 q^{-5} +25016 q^{-6} -17662 q^{-7} -41084 q^{-8} -26662 q^{-9} +9036 q^{-10} +32799 q^{-11} +25672 q^{-12} -1989 q^{-13} -23822 q^{-14} -22464 q^{-15} -2828 q^{-16} +15585 q^{-17} +17807 q^{-18} +5172 q^{-19} -8907 q^{-20} -12742 q^{-21} -5576 q^{-22} +4252 q^{-23} +8230 q^{-24} +4732 q^{-25} -1508 q^{-26} -4774 q^{-27} -3377 q^{-28} +174 q^{-29} +2460 q^{-30} +2115 q^{-31} +284 q^{-32} -1133 q^{-33} -1170 q^{-34} -306 q^{-35} +453 q^{-36} +563 q^{-37} +213 q^{-38} -137 q^{-39} -255 q^{-40} -129 q^{-41} +55 q^{-42} +92 q^{-43} +40 q^{-44} +11 q^{-45} -27 q^{-46} -41 q^{-47} +9 q^{-48} +14 q^{-49} -7 q^{-50} +11 q^{-51} +3 q^{-52} -12 q^{-53} +2 q^{-54} +4 q^{-55} -4 q^{-56} +2 q^{-57} +2 q^{-58} -3 q^{-59} + q^{-60} </math> \|		coloured_jones_5 = <math>q^{90}-4 q^{89}+q^{88}+9 q^{87}-q^{86}-4 q^{85}-10 q^{84}-20 q^{83}-3 q^{82}+53 q^{81}+57 q^{80}+9 q^{79}-65 q^{78}-151 q^{77}-129 q^{76}+63 q^{75}+320 q^{74}+351 q^{73}+81 q^{72}-395 q^{71}-767 q^{70}-571 q^{69}+300 q^{68}+1236 q^{67}+1361 q^{66}+362 q^{65}-1364 q^{64}-2524 q^{63}-1744 q^{62}+845 q^{61}+3444 q^{60}+3784 q^{59}+944 q^{58}-3570 q^{57}-6123 q^{56}-3944 q^{55}+2142 q^{54}+7801 q^{53}+7945 q^{52}+1232 q^{51}-7936 q^{50}-12002 q^{49}-6459 q^{48}+5733 q^{47}+15075 q^{46}+12790 q^{45}-987 q^{44}-16028 q^{43}-19243 q^{42}-5945 q^{41}+14406 q^{40}+24602 q^{39}+14131 q^{38}-10120 q^{37}-28002 q^{36}-22616 q^{35}+3740 q^{34}+29233 q^{33}+30312 q^{32}+3785 q^{31}-28199 q^{30}-36688 q^{29}-11811 q^{28}+25764 q^{27}+41502 q^{26}+19260 q^{25}-22173 q^{24}-44870 q^{23}-26171 q^{22}+18380 q^{21}+47190 q^{20}+31969 q^{19}-14339 q^{18}-48648 q^{17}-37297 q^{16}+10504 q^{15}+49507 q^{14}+41817 q^{13}-6259 q^{12}-49591 q^{11}-46135 q^{10}+1776 q^9+48605 q^8+49590 q^7+3628 q^6-46021 q^5-52288 q^4-9434 q^3+41535 q^2+53054 q+15615-34918 q^{-1} -51744 q^{-2} -21076 q^{-3} +26730 q^{-4} +47626 q^{-5} +25016 q^{-6} -17662 q^{-7} -41084 q^{-8} -26662 q^{-9} +9036 q^{-10} +32799 q^{-11} +25672 q^{-12} -1989 q^{-13} -23822 q^{-14} -22464 q^{-15} -2828 q^{-16} +15585 q^{-17} +17807 q^{-18} +5172 q^{-19} -8907 q^{-20} -12742 q^{-21} -5576 q^{-22} +4252 q^{-23} +8230 q^{-24} +4732 q^{-25} -1508 q^{-26} -4774 q^{-27} -3377 q^{-28} +174 q^{-29} +2460 q^{-30} +2115 q^{-31} +284 q^{-32} -1133 q^{-33} -1170 q^{-34} -306 q^{-35} +453 q^{-36} +563 q^{-37} +213 q^{-38} -137 q^{-39} -255 q^{-40} -129 q^{-41} +55 q^{-42} +92 q^{-43} +40 q^{-44} +11 q^{-45} -27 q^{-46} -41 q^{-47} +9 q^{-48} +14 q^{-49} -7 q^{-50} +11 q^{-51} +3 q^{-52} -12 q^{-53} +2 q^{-54} +4 q^{-55} -4 q^{-56} +2 q^{-57} +2 q^{-58} -3 q^{-59} + q^{-60} </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, 87]]</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, 87]]</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],
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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>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, 87]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_87_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, 87]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_87_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, 87]]&) /@ {~~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, 87]]&) /@ {
			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>{Chiral, 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>{Chiral, 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, 87]][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, 87]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:38, 30 August 2005

2005-08-30T14:38:19Z

Show changes

DrorsRobot at 01:05, 30 August 2005

2005-08-30T01:05:46Z

← Older revision		Revision as of 21:05, 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 22:20, 29 August 2005

2005-08-29T22:20:52Z

Show changes

ScottTestRobot at 00:11, 29 August 2005

2005-08-29T00:11:47Z

← Older revision		Revision as of 20:11, 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=87\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,3,-6,5,-7,10,-2,7,-9,8,-3,4,-5,9,-8,6,-4/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=87\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,3,-6,5,-7,10,-2,7,-9,8,-3,4,-5,9,-8,6,-4/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>-7</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>-7</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>-9</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>-9</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 01:48, 28 August 2005

2005-08-28T01:48:28Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:36Z

Resetting knot page to basic template.

New page

10 87 - Revision history

ScottTestRobot at 22:02, 1 September 2005

DrorsRobot at 22:48, 31 August 2005

ScottKnotPageRobot at 14:38, 30 August 2005

DrorsRobot at 01:05, 30 August 2005

DrorsRobot at 22:20, 29 August 2005

ScottTestRobot at 00:11, 29 August 2005

ScottTestRobot at 01:48, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.