9 48 - Revision history

ScottTestRobot at 21:58, 1 September 2005

2005-09-01T21:58:22Z

DrorsRobot at 22:42, 31 August 2005

2005-08-31T22:42:10Z

← Older revision		Revision as of 18:42, 31 August 2005
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	{{Rolfsen Knot Page\|		{{Rolfsen Knot Page\|
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	coloured_jones_3 = <math>-2 q^{35}+q^{33}+9 q^{32}-5 q^{31}-12 q^{30}-q^{29}+27 q^{28}+5 q^{27}-37 q^{26}-19 q^{25}+49 q^{24}+32 q^{23}-58 q^{22}-50 q^{21}+61 q^{20}+68 q^{19}-67 q^{18}-74 q^{17}+58 q^{16}+92 q^{15}-62 q^{14}-86 q^{13}+47 q^{12}+94 q^{11}-44 q^{10}-83 q^9+26 q^8+79 q^7-15 q^6-67 q^5+2 q^4+53 q^3+8 q^2-37 q-12+22 q^{-1} +14 q^{-2} -13 q^{-3} -9 q^{-4} +4 q^{-5} +5 q^{-6} -3 q^{-8} + q^{-9} </math> \|		coloured_jones_3 = <math>-2 q^{35}+q^{33}+9 q^{32}-5 q^{31}-12 q^{30}-q^{29}+27 q^{28}+5 q^{27}-37 q^{26}-19 q^{25}+49 q^{24}+32 q^{23}-58 q^{22}-50 q^{21}+61 q^{20}+68 q^{19}-67 q^{18}-74 q^{17}+58 q^{16}+92 q^{15}-62 q^{14}-86 q^{13}+47 q^{12}+94 q^{11}-44 q^{10}-83 q^9+26 q^8+79 q^7-15 q^6-67 q^5+2 q^4+53 q^3+8 q^2-37 q-12+22 q^{-1} +14 q^{-2} -13 q^{-3} -9 q^{-4} +4 q^{-5} +5 q^{-6} -3 q^{-8} + q^{-9} </math> \|
	coloured_jones_4 = <math>q^{58}+2 q^{57}-6 q^{55}-4 q^{54}-5 q^{53}+14 q^{52}+21 q^{51}-9 q^{50}-20 q^{49}-46 q^{48}+20 q^{47}+76 q^{46}+25 q^{45}-23 q^{44}-137 q^{43}-25 q^{42}+133 q^{41}+109 q^{40}+30 q^{39}-242 q^{38}-127 q^{37}+145 q^{36}+208 q^{35}+136 q^{34}-314 q^{33}-238 q^{32}+114 q^{31}+273 q^{30}+247 q^{29}-336 q^{28}-312 q^{27}+66 q^{26}+293 q^{25}+324 q^{24}-321 q^{23}-342 q^{22}+18 q^{21}+278 q^{20}+353 q^{19}-269 q^{18}-327 q^{17}-36 q^{16}+222 q^{15}+350 q^{14}-178 q^{13}-268 q^{12}-93 q^{11}+127 q^{10}+306 q^9-70 q^8-166 q^7-119 q^6+22 q^5+213 q^4+6 q^3-58 q^2-90 q-41+102 q^{-1} +24 q^{-2} +5 q^{-3} -39 q^{-4} -40 q^{-5} +31 q^{-6} +9 q^{-7} +14 q^{-8} -6 q^{-9} -16 q^{-10} +4 q^{-11} +5 q^{-13} -3 q^{-15} + q^{-16} </math> \|		coloured_jones_4 = <math>q^{58}+2 q^{57}-6 q^{55}-4 q^{54}-5 q^{53}+14 q^{52}+21 q^{51}-9 q^{50}-20 q^{49}-46 q^{48}+20 q^{47}+76 q^{46}+25 q^{45}-23 q^{44}-137 q^{43}-25 q^{42}+133 q^{41}+109 q^{40}+30 q^{39}-242 q^{38}-127 q^{37}+145 q^{36}+208 q^{35}+136 q^{34}-314 q^{33}-238 q^{32}+114 q^{31}+273 q^{30}+247 q^{29}-336 q^{28}-312 q^{27}+66 q^{26}+293 q^{25}+324 q^{24}-321 q^{23}-342 q^{22}+18 q^{21}+278 q^{20}+353 q^{19}-269 q^{18}-327 q^{17}-36 q^{16}+222 q^{15}+350 q^{14}-178 q^{13}-268 q^{12}-93 q^{11}+127 q^{10}+306 q^9-70 q^8-166 q^7-119 q^6+22 q^5+213 q^4+6 q^3-58 q^2-90 q-41+102 q^{-1} +24 q^{-2} +5 q^{-3} -39 q^{-4} -40 q^{-5} +31 q^{-6} +9 q^{-7} +14 q^{-8} -6 q^{-9} -16 q^{-10} +4 q^{-11} +5 q^{-13} -3 q^{-15} + q^{-16} </math> \|
	coloured_jones_5 = \|		coloured_jones_5 = <math>\textrm{NotAvailable}(q)</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, 48]]</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, 48]]</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[12, 8, 13, 7], X[3, 11, 4, 10], X[11, 3, 12, 2],		<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[12, 8, 13, 7], X[3, 11, 4, 10], X[11, 3, 12, 2],
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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[9, 48]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_48_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, 48]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_48_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, 48]]&) /@ {~~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, 48]]&) /@ {
			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, 2, 3, {4, 6}, 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, 2, 2, 3, {4, 6}, 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[9, 48]][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, 48]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:34, 30 August 2005

2005-08-30T14:34:18Z

Show changes

DrorsRobot at 01:01, 30 August 2005

2005-08-30T01:01:16Z

← Older revision		Revision as of 21:01, 29 August 2005
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	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}}
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	[[Category:Knot Page]]		[[Category:Knot Page]]

DrorsRobot at 22:00, 29 August 2005

2005-08-29T22:00:55Z

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ScottTestRobot at 00:06, 29 August 2005

2005-08-29T00:06:54Z

← Older revision		Revision as of 20:06, 28 August 2005
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	{{Knot Navigation Links\|ext=gif}}		{{Knot Navigation Links\|ext=gif}}

		⚫	{{Rolfsen Knot Page Header\|n=9\|k=48\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,5,-6,2,9,-8,3,-4,-2,6,-5,-7,8,-9,7/goTop.html}}
	{\| align=left
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⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=9\|k=48\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,5,-6,2,9,-8,3,-4,-2,6,-5,-7,8,-9,7/goTop.html}}
	\|{{:{{PAGENAME}} Quick Notes}}
	\|}

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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>.

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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>-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>-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>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>1</td></tr>
	</table>~~</center>~~		</table>}}

	{{Computer Talk Header}}		{{Computer Talk Header}}

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	q t + 3 q t + 2 q t + q t + 2 q t</nowiki></pre></td></tr>		q t + 3 q t + 2 q t + q t + 2 q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:45, 28 August 2005

2005-08-28T01:45:15Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T21:22:40Z

Resetting knot page to basic template.

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