ScottTestRobot at 22:02, 1 September 2005

2005-09-01T22:02:49Z

DrorsRobot at 22:48, 31 August 2005

2005-08-31T22:48:52Z

← Older revision		Revision as of 18:48, 31 August 2005
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	coloured_jones_4 = <math>q^{26}-5 q^{25}+5 q^{24}+10 q^{23}-16 q^{22}-2 q^{21}-25 q^{20}+52 q^{19}+82 q^{18}-106 q^{17}-97 q^{16}-176 q^{15}+289 q^{14}+590 q^{13}-173 q^{12}-644 q^{11}-1236 q^{10}+481 q^9+2406 q^8+1127 q^7-1182 q^6-4720 q^5-1616 q^4+4894 q^3+5955 q^2+1523 q-9653-8735 q^{-1} +3822 q^{-2} +12915 q^{-3} +10561 q^{-4} -11015 q^{-5} -18889 q^{-6} -4083 q^{-7} +16524 q^{-8} +23284 q^{-9} -5597 q^{-10} -26135 q^{-11} -15946 q^{-12} +13781 q^{-13} +33559 q^{-14} +3832 q^{-15} -27397 q^{-16} -26171 q^{-17} +7018 q^{-18} +38261 q^{-19} +12749 q^{-20} -24101 q^{-21} -32180 q^{-22} -530 q^{-23} +37954 q^{-24} +19437 q^{-25} -18052 q^{-26} -34142 q^{-27} -7995 q^{-28} +33219 q^{-29} +23876 q^{-30} -9405 q^{-31} -31723 q^{-32} -14982 q^{-33} +23705 q^{-34} +24646 q^{-35} +813 q^{-36} -23810 q^{-37} -18806 q^{-38} +11021 q^{-39} +19624 q^{-40} +8483 q^{-41} -12097 q^{-42} -16370 q^{-43} +500 q^{-44} +10327 q^{-45} +9553 q^{-46} -2283 q^{-47} -9179 q^{-48} -3362 q^{-49} +2438 q^{-50} +5538 q^{-51} +1493 q^{-52} -2867 q^{-53} -2180 q^{-54} -533 q^{-55} +1685 q^{-56} +1111 q^{-57} -354 q^{-58} -528 q^{-59} -477 q^{-60} +247 q^{-61} +278 q^{-62} -6 q^{-63} -26 q^{-64} -111 q^{-65} +25 q^{-66} +36 q^{-67} -10 q^{-68} +6 q^{-69} -13 q^{-70} +5 q^{-71} +4 q^{-72} -4 q^{-73} + q^{-74} </math> \|		coloured_jones_4 = <math>q^{26}-5 q^{25}+5 q^{24}+10 q^{23}-16 q^{22}-2 q^{21}-25 q^{20}+52 q^{19}+82 q^{18}-106 q^{17}-97 q^{16}-176 q^{15}+289 q^{14}+590 q^{13}-173 q^{12}-644 q^{11}-1236 q^{10}+481 q^9+2406 q^8+1127 q^7-1182 q^6-4720 q^5-1616 q^4+4894 q^3+5955 q^2+1523 q-9653-8735 q^{-1} +3822 q^{-2} +12915 q^{-3} +10561 q^{-4} -11015 q^{-5} -18889 q^{-6} -4083 q^{-7} +16524 q^{-8} +23284 q^{-9} -5597 q^{-10} -26135 q^{-11} -15946 q^{-12} +13781 q^{-13} +33559 q^{-14} +3832 q^{-15} -27397 q^{-16} -26171 q^{-17} +7018 q^{-18} +38261 q^{-19} +12749 q^{-20} -24101 q^{-21} -32180 q^{-22} -530 q^{-23} +37954 q^{-24} +19437 q^{-25} -18052 q^{-26} -34142 q^{-27} -7995 q^{-28} +33219 q^{-29} +23876 q^{-30} -9405 q^{-31} -31723 q^{-32} -14982 q^{-33} +23705 q^{-34} +24646 q^{-35} +813 q^{-36} -23810 q^{-37} -18806 q^{-38} +11021 q^{-39} +19624 q^{-40} +8483 q^{-41} -12097 q^{-42} -16370 q^{-43} +500 q^{-44} +10327 q^{-45} +9553 q^{-46} -2283 q^{-47} -9179 q^{-48} -3362 q^{-49} +2438 q^{-50} +5538 q^{-51} +1493 q^{-52} -2867 q^{-53} -2180 q^{-54} -533 q^{-55} +1685 q^{-56} +1111 q^{-57} -354 q^{-58} -528 q^{-59} -477 q^{-60} +247 q^{-61} +278 q^{-62} -6 q^{-63} -26 q^{-64} -111 q^{-65} +25 q^{-66} +36 q^{-67} -10 q^{-68} +6 q^{-69} -13 q^{-70} +5 q^{-71} +4 q^{-72} -4 q^{-73} + q^{-74} </math> \|
	coloured_jones_5 = <math>-q^{40}+5 q^{39}-5 q^{38}-10 q^{37}+16 q^{36}+7 q^{35}-5 q^{34}-8 q^{33}-34 q^{32}-29 q^{31}+90 q^{30}+149 q^{29}+4 q^{28}-230 q^{27}-408 q^{26}-195 q^{25}+497 q^{24}+1219 q^{23}+903 q^{22}-872 q^{21}-2763 q^{20}-2813 q^{19}+293 q^{18}+5211 q^{17}+7390 q^{16}+2485 q^{15}-7674 q^{14}-14877 q^{13}-10397 q^{12}+7132 q^{11}+25362 q^{10}+25619 q^9+298 q^8-34927 q^7-48831 q^6-19965 q^5+37974 q^4+77330 q^3+54320 q^2-26923 q-104297-102435 q^{-1} -3736 q^{-2} +120534 q^{-3} +158188 q^{-4} +55648 q^{-5} -118030 q^{-6} -211957 q^{-7} -124190 q^{-8} +91957 q^{-9} +253523 q^{-10} +201274 q^{-11} -44019 q^{-12} -275896 q^{-13} -275665 q^{-14} -19871 q^{-15} +276333 q^{-16} +338995 q^{-17} +90509 q^{-18} -257884 q^{-19} -385285 q^{-20} -159267 q^{-21} +225845 q^{-22} +414167 q^{-23} +219600 q^{-24} -187091 q^{-25} -427285 q^{-26} -269102 q^{-27} +146528 q^{-28} +429225 q^{-29} +307561 q^{-30} -107164 q^{-31} -422549 q^{-32} -337731 q^{-33} +68646 q^{-34} +410235 q^{-35} +361491 q^{-36} -29850 q^{-37} -390960 q^{-38} -380646 q^{-39} -12099 q^{-40} +363719 q^{-41} +394335 q^{-42} +57800 q^{-43} -325057 q^{-44} -399728 q^{-45} -106875 q^{-46} +273351 q^{-47} +392638 q^{-48} +155175 q^{-49} -208778 q^{-50} -368727 q^{-51} -196351 q^{-52} +135017 q^{-53} +325835 q^{-54} +223155 q^{-55} -59569 q^{-56} -265676 q^{-57} -229518 q^{-58} -7919 q^{-59} +194245 q^{-60} +213473 q^{-61} +58443 q^{-62} -121321 q^{-63} -178297 q^{-64} -86326 q^{-65} +57493 q^{-66} +131709 q^{-67} +91411 q^{-68} -10429 q^{-69} -83915 q^{-70} -79185 q^{-71} -16583 q^{-72} +43794 q^{-73} +57614 q^{-74} +26168 q^{-75} -15987 q^{-76} -35432 q^{-77} -24141 q^{-78} +1065 q^{-79} +17892 q^{-80} +16938 q^{-81} +4466 q^{-82} -6938 q^{-83} -9673 q^{-84} -4710 q^{-85} +1710 q^{-86} +4482 q^{-87} +3074 q^{-88} +140 q^{-89} -1652 q^{-90} -1582 q^{-91} -417 q^{-92} +523 q^{-93} +628 q^{-94} +230 q^{-95} -100 q^{-96} -196 q^{-97} -131 q^{-98} +32 q^{-99} +78 q^{-100} +10 q^{-101} -7 q^{-102} - q^{-103} -14 q^{-104} - q^{-105} +13 q^{-106} -5 q^{-107} -4 q^{-108} +4 q^{-109} - q^{-110} </math> \|		coloured_jones_5 = <math>-q^{40}+5 q^{39}-5 q^{38}-10 q^{37}+16 q^{36}+7 q^{35}-5 q^{34}-8 q^{33}-34 q^{32}-29 q^{31}+90 q^{30}+149 q^{29}+4 q^{28}-230 q^{27}-408 q^{26}-195 q^{25}+497 q^{24}+1219 q^{23}+903 q^{22}-872 q^{21}-2763 q^{20}-2813 q^{19}+293 q^{18}+5211 q^{17}+7390 q^{16}+2485 q^{15}-7674 q^{14}-14877 q^{13}-10397 q^{12}+7132 q^{11}+25362 q^{10}+25619 q^9+298 q^8-34927 q^7-48831 q^6-19965 q^5+37974 q^4+77330 q^3+54320 q^2-26923 q-104297-102435 q^{-1} -3736 q^{-2} +120534 q^{-3} +158188 q^{-4} +55648 q^{-5} -118030 q^{-6} -211957 q^{-7} -124190 q^{-8} +91957 q^{-9} +253523 q^{-10} +201274 q^{-11} -44019 q^{-12} -275896 q^{-13} -275665 q^{-14} -19871 q^{-15} +276333 q^{-16} +338995 q^{-17} +90509 q^{-18} -257884 q^{-19} -385285 q^{-20} -159267 q^{-21} +225845 q^{-22} +414167 q^{-23} +219600 q^{-24} -187091 q^{-25} -427285 q^{-26} -269102 q^{-27} +146528 q^{-28} +429225 q^{-29} +307561 q^{-30} -107164 q^{-31} -422549 q^{-32} -337731 q^{-33} +68646 q^{-34} +410235 q^{-35} +361491 q^{-36} -29850 q^{-37} -390960 q^{-38} -380646 q^{-39} -12099 q^{-40} +363719 q^{-41} +394335 q^{-42} +57800 q^{-43} -325057 q^{-44} -399728 q^{-45} -106875 q^{-46} +273351 q^{-47} +392638 q^{-48} +155175 q^{-49} -208778 q^{-50} -368727 q^{-51} -196351 q^{-52} +135017 q^{-53} +325835 q^{-54} +223155 q^{-55} -59569 q^{-56} -265676 q^{-57} -229518 q^{-58} -7919 q^{-59} +194245 q^{-60} +213473 q^{-61} +58443 q^{-62} -121321 q^{-63} -178297 q^{-64} -86326 q^{-65} +57493 q^{-66} +131709 q^{-67} +91411 q^{-68} -10429 q^{-69} -83915 q^{-70} -79185 q^{-71} -16583 q^{-72} +43794 q^{-73} +57614 q^{-74} +26168 q^{-75} -15987 q^{-76} -35432 q^{-77} -24141 q^{-78} +1065 q^{-79} +17892 q^{-80} +16938 q^{-81} +4466 q^{-82} -6938 q^{-83} -9673 q^{-84} -4710 q^{-85} +1710 q^{-86} +4482 q^{-87} +3074 q^{-88} +140 q^{-89} -1652 q^{-90} -1582 q^{-91} -417 q^{-92} +523 q^{-93} +628 q^{-94} +230 q^{-95} -100 q^{-96} -196 q^{-97} -131 q^{-98} +32 q^{-99} +78 q^{-100} +10 q^{-101} -7 q^{-102} - q^{-103} -14 q^{-104} - q^{-105} +13 q^{-106} -5 q^{-107} -4 q^{-108} +4 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, 121]]</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, 121]]</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, 6, 2, 7], X[7, 20, 8, 1], X[9, 19, 10, 18], X[3, 11, 4, 10],		<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, 6, 2, 7], X[7, 20, 8, 1], X[9, 19, 10, 18], X[3, 11, 4, 10],
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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, 121]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_121_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, 121]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_121_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, 121]]&) /@ {~~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, 121]]&) /@ {
			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, 121]][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, 121]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:38, 30 August 2005

2005-08-30T14:38:44Z

Show changes

DrorsRobot at 01:06, 30 August 2005

2005-08-30T01:06:16Z

← Older revision		Revision as of 21:06, 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 22:23, 29 August 2005

2005-08-29T22:23:55Z

Show changes

ScottTestRobot at 00:12, 29 August 2005

2005-08-29T00:12:16Z

← Older revision		Revision as of 20:12, 28 August 2005
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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=121\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-4,5,-6,1,-2,9,-3,4,-7,6,-9,8,-10,7,-5,3,-8,2/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=121\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-4,5,-6,1,-2,9,-3,4,-7,6,-9,8,-10,7,-5,3,-8,2/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>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>-15</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>-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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	4 q t + q t</nowiki></pre></td></tr>		4 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:48, 28 August 2005

2005-08-28T01:48:56Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:07Z

Resetting knot page to basic template.

New page

10 121 - 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 01:06, 30 August 2005

DrorsRobot at 22:23, 29 August 2005

ScottTestRobot at 00:12, 29 August 2005

ScottTestRobot at 01:48, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.