ScottTestRobot at 22:05, 1 September 2005

2005-09-01T22:05:23Z

DrorsRobot at 22:53, 31 August 2005

2005-08-31T22:53:59Z

← Older revision		Revision as of 18:53, 31 August 2005
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	coloured_jones_4 = <math>q^{26}-3 q^{25}+q^{24}+3 q^{23}-3 q^{22}+8 q^{21}-13 q^{20}+4 q^{19}+10 q^{18}-22 q^{17}+23 q^{16}-31 q^{15}+37 q^{14}+51 q^{13}-87 q^{12}-11 q^{11}-118 q^{10}+139 q^9+266 q^8-89 q^7-145 q^6-530 q^5+104 q^4+745 q^3+349 q^2-49 q-1367-581 q^{-1} +1017 q^{-2} +1331 q^{-3} +904 q^{-4} -2048 q^{-5} -1988 q^{-6} +391 q^{-7} +2211 q^{-8} +2680 q^{-9} -1864 q^{-10} -3361 q^{-11} -1064 q^{-12} +2315 q^{-13} +4453 q^{-14} -909 q^{-15} -4017 q^{-16} -2574 q^{-17} +1732 q^{-18} +5532 q^{-19} +193 q^{-20} -3945 q^{-21} -3591 q^{-22} +902 q^{-23} +5841 q^{-24} +1109 q^{-25} -3391 q^{-26} -4083 q^{-27} -19 q^{-28} +5474 q^{-29} +1887 q^{-30} -2375 q^{-31} -4093 q^{-32} -1071 q^{-33} +4375 q^{-34} +2426 q^{-35} -908 q^{-36} -3412 q^{-37} -1987 q^{-38} +2599 q^{-39} +2318 q^{-40} +541 q^{-41} -2028 q^{-42} -2182 q^{-43} +794 q^{-44} +1428 q^{-45} +1195 q^{-46} -569 q^{-47} -1493 q^{-48} -198 q^{-49} +378 q^{-50} +908 q^{-51} +181 q^{-52} -592 q^{-53} -278 q^{-54} -124 q^{-55} +354 q^{-56} +216 q^{-57} -121 q^{-58} -77 q^{-59} -126 q^{-60} +74 q^{-61} +73 q^{-62} -20 q^{-63} +5 q^{-64} -39 q^{-65} +12 q^{-66} +14 q^{-67} -9 q^{-68} +5 q^{-69} -6 q^{-70} +3 q^{-71} +2 q^{-72} -3 q^{-73} + q^{-74} </math> \|		coloured_jones_4 = <math>q^{26}-3 q^{25}+q^{24}+3 q^{23}-3 q^{22}+8 q^{21}-13 q^{20}+4 q^{19}+10 q^{18}-22 q^{17}+23 q^{16}-31 q^{15}+37 q^{14}+51 q^{13}-87 q^{12}-11 q^{11}-118 q^{10}+139 q^9+266 q^8-89 q^7-145 q^6-530 q^5+104 q^4+745 q^3+349 q^2-49 q-1367-581 q^{-1} +1017 q^{-2} +1331 q^{-3} +904 q^{-4} -2048 q^{-5} -1988 q^{-6} +391 q^{-7} +2211 q^{-8} +2680 q^{-9} -1864 q^{-10} -3361 q^{-11} -1064 q^{-12} +2315 q^{-13} +4453 q^{-14} -909 q^{-15} -4017 q^{-16} -2574 q^{-17} +1732 q^{-18} +5532 q^{-19} +193 q^{-20} -3945 q^{-21} -3591 q^{-22} +902 q^{-23} +5841 q^{-24} +1109 q^{-25} -3391 q^{-26} -4083 q^{-27} -19 q^{-28} +5474 q^{-29} +1887 q^{-30} -2375 q^{-31} -4093 q^{-32} -1071 q^{-33} +4375 q^{-34} +2426 q^{-35} -908 q^{-36} -3412 q^{-37} -1987 q^{-38} +2599 q^{-39} +2318 q^{-40} +541 q^{-41} -2028 q^{-42} -2182 q^{-43} +794 q^{-44} +1428 q^{-45} +1195 q^{-46} -569 q^{-47} -1493 q^{-48} -198 q^{-49} +378 q^{-50} +908 q^{-51} +181 q^{-52} -592 q^{-53} -278 q^{-54} -124 q^{-55} +354 q^{-56} +216 q^{-57} -121 q^{-58} -77 q^{-59} -126 q^{-60} +74 q^{-61} +73 q^{-62} -20 q^{-63} +5 q^{-64} -39 q^{-65} +12 q^{-66} +14 q^{-67} -9 q^{-68} +5 q^{-69} -6 q^{-70} +3 q^{-71} +2 q^{-72} -3 q^{-73} + q^{-74} </math> \|
	coloured_jones_5 = <math>-q^{40}+3 q^{39}-q^{38}-3 q^{37}+3 q^{36}-3 q^{35}-5 q^{34}+9 q^{33}+6 q^{32}-6 q^{31}+11 q^{30}-5 q^{29}-31 q^{28}-12 q^{27}+8 q^{26}+27 q^{25}+72 q^{24}+56 q^{23}-65 q^{22}-174 q^{21}-161 q^{20}-q^{19}+298 q^{18}+459 q^{17}+219 q^{16}-385 q^{15}-899 q^{14}-761 q^{13}+192 q^{12}+1400 q^{11}+1756 q^{10}+564 q^9-1671 q^8-3127 q^7-2139 q^6+1184 q^5+4518 q^4+4662 q^3+529 q^2-5289 q-7834-3775 q^{-1} +4744 q^{-2} +10896 q^{-3} +8472 q^{-4} -2221 q^{-5} -13154 q^{-6} -14015 q^{-7} -2144 q^{-8} +13593 q^{-9} +19434 q^{-10} +8337 q^{-11} -12153 q^{-12} -23999 q^{-13} -15026 q^{-14} +8685 q^{-15} +26814 q^{-16} +21869 q^{-17} -4042 q^{-18} -28061 q^{-19} -27448 q^{-20} -1273 q^{-21} +27591 q^{-22} +31996 q^{-23} +6247 q^{-24} -26227 q^{-25} -34797 q^{-26} -10731 q^{-27} +24132 q^{-28} +36701 q^{-29} +14253 q^{-30} -21994 q^{-31} -37381 q^{-32} -17209 q^{-33} +19591 q^{-34} +37727 q^{-35} +19581 q^{-36} -17184 q^{-37} -37280 q^{-38} -21810 q^{-39} +14232 q^{-40} +36397 q^{-41} +23911 q^{-42} -10754 q^{-43} -34576 q^{-44} -25775 q^{-45} +6436 q^{-46} +31610 q^{-47} +27167 q^{-48} -1485 q^{-49} -27347 q^{-50} -27508 q^{-51} -3652 q^{-52} +21653 q^{-53} +26442 q^{-54} +8385 q^{-55} -15075 q^{-56} -23661 q^{-57} -11847 q^{-58} +8232 q^{-59} +19270 q^{-60} +13533 q^{-61} -2099 q^{-62} -13857 q^{-63} -13171 q^{-64} -2526 q^{-65} +8308 q^{-66} +11063 q^{-67} +5126 q^{-68} -3476 q^{-69} -7946 q^{-70} -5816 q^{-71} +105 q^{-72} +4713 q^{-73} +4988 q^{-74} +1705 q^{-75} -2036 q^{-76} -3525 q^{-77} -2172 q^{-78} +373 q^{-79} +1989 q^{-80} +1817 q^{-81} +431 q^{-82} -877 q^{-83} -1195 q^{-84} -581 q^{-85} +241 q^{-86} +640 q^{-87} +446 q^{-88} +5 q^{-89} -261 q^{-90} -266 q^{-91} -77 q^{-92} +109 q^{-93} +125 q^{-94} +36 q^{-95} -21 q^{-96} -41 q^{-97} -37 q^{-98} +12 q^{-99} +25 q^{-100} -2 q^{-101} -3 q^{-102} +3 q^{-103} -6 q^{-104} - q^{-105} +6 q^{-106} -3 q^{-107} -2 q^{-108} +3 q^{-109} - q^{-110} </math> \|		coloured_jones_5 = <math>-q^{40}+3 q^{39}-q^{38}-3 q^{37}+3 q^{36}-3 q^{35}-5 q^{34}+9 q^{33}+6 q^{32}-6 q^{31}+11 q^{30}-5 q^{29}-31 q^{28}-12 q^{27}+8 q^{26}+27 q^{25}+72 q^{24}+56 q^{23}-65 q^{22}-174 q^{21}-161 q^{20}-q^{19}+298 q^{18}+459 q^{17}+219 q^{16}-385 q^{15}-899 q^{14}-761 q^{13}+192 q^{12}+1400 q^{11}+1756 q^{10}+564 q^9-1671 q^8-3127 q^7-2139 q^6+1184 q^5+4518 q^4+4662 q^3+529 q^2-5289 q-7834-3775 q^{-1} +4744 q^{-2} +10896 q^{-3} +8472 q^{-4} -2221 q^{-5} -13154 q^{-6} -14015 q^{-7} -2144 q^{-8} +13593 q^{-9} +19434 q^{-10} +8337 q^{-11} -12153 q^{-12} -23999 q^{-13} -15026 q^{-14} +8685 q^{-15} +26814 q^{-16} +21869 q^{-17} -4042 q^{-18} -28061 q^{-19} -27448 q^{-20} -1273 q^{-21} +27591 q^{-22} +31996 q^{-23} +6247 q^{-24} -26227 q^{-25} -34797 q^{-26} -10731 q^{-27} +24132 q^{-28} +36701 q^{-29} +14253 q^{-30} -21994 q^{-31} -37381 q^{-32} -17209 q^{-33} +19591 q^{-34} +37727 q^{-35} +19581 q^{-36} -17184 q^{-37} -37280 q^{-38} -21810 q^{-39} +14232 q^{-40} +36397 q^{-41} +23911 q^{-42} -10754 q^{-43} -34576 q^{-44} -25775 q^{-45} +6436 q^{-46} +31610 q^{-47} +27167 q^{-48} -1485 q^{-49} -27347 q^{-50} -27508 q^{-51} -3652 q^{-52} +21653 q^{-53} +26442 q^{-54} +8385 q^{-55} -15075 q^{-56} -23661 q^{-57} -11847 q^{-58} +8232 q^{-59} +19270 q^{-60} +13533 q^{-61} -2099 q^{-62} -13857 q^{-63} -13171 q^{-64} -2526 q^{-65} +8308 q^{-66} +11063 q^{-67} +5126 q^{-68} -3476 q^{-69} -7946 q^{-70} -5816 q^{-71} +105 q^{-72} +4713 q^{-73} +4988 q^{-74} +1705 q^{-75} -2036 q^{-76} -3525 q^{-77} -2172 q^{-78} +373 q^{-79} +1989 q^{-80} +1817 q^{-81} +431 q^{-82} -877 q^{-83} -1195 q^{-84} -581 q^{-85} +241 q^{-86} +640 q^{-87} +446 q^{-88} +5 q^{-89} -261 q^{-90} -266 q^{-91} -77 q^{-92} +109 q^{-93} +125 q^{-94} +36 q^{-95} -21 q^{-96} -41 q^{-97} -37 q^{-98} +12 q^{-99} +25 q^{-100} -2 q^{-101} -3 q^{-102} +3 q^{-103} -6 q^{-104} - q^{-105} +6 q^{-106} -3 q^{-107} -2 q^{-108} +3 q^{-109} - q^{-110} </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, 103]]</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, 103]]</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[6, 2, 7, 1], X[18, 6, 19, 5], X[20, 13, 1, 14], X[16, 7, 17, 8],		<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[6, 2, 7, 1], X[18, 6, 19, 5], X[20, 13, 1, 14], X[16, 7, 17, 8],
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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, 103]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_103_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, 103]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_103_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, 103]]&) /@ {~~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, 103]]&) /@ {
			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, 3, 3, 3, NotAvailable, 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, 3, 3, 3, NotAvailable, 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[10, 103]][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, 103]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:41, 30 August 2005

2005-08-30T14:41:25Z

Show changes

DrorsRobot at 01:09, 30 August 2005

2005-08-30T01:09:22Z

← Older revision		Revision as of 21:09, 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 22:21, 29 August 2005

2005-08-29T22:21:53Z

Show changes

ScottTestRobot at 00:15, 29 August 2005

2005-08-29T00:15:45Z

← Older revision		Revision as of 20:15, 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=103\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,5,-6,2,-1,4,-8,7,-5,6,-9,3,-7,8,-4,10,-2,9,-3/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=103\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,5,-6,2,-1,4,-8,7,-5,6,-9,3,-7,8,-4,10,-2,9,-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>
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	<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>-15</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>-15</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>-17</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>-17</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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	2 q t + q t</nowiki></pre></td></tr>		2 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:52, 28 August 2005

2005-08-28T01:52:03Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:51Z

Resetting knot page to basic template.

New page

10 103 - 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 01:09, 30 August 2005

DrorsRobot at 22:21, 29 August 2005

ScottTestRobot at 00:15, 29 August 2005

ScottTestRobot at 01:52, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.