ScottTestRobot at 22:02, 1 September 2005

2005-09-01T22:02:00Z

DrorsRobot at 22:47, 31 August 2005

2005-08-31T22:47:29Z

← Older revision		Revision as of 18:47, 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 41:		Line 44:
	coloured_jones_5 = <math>-2 q^{46}+5 q^{44}+5 q^{43}-5 q^{41}-22 q^{40}-17 q^{39}+15 q^{38}+45 q^{37}+49 q^{36}+12 q^{35}-76 q^{34}-134 q^{33}-71 q^{32}+90 q^{31}+239 q^{30}+211 q^{29}-37 q^{28}-358 q^{27}-443 q^{26}-104 q^{25}+444 q^{24}+713 q^{23}+383 q^{22}-417 q^{21}-1034 q^{20}-774 q^{19}+299 q^{18}+1271 q^{17}+1238 q^{16}-9 q^{15}-1457 q^{14}-1706 q^{13}-348 q^{12}+1497 q^{11}+2121 q^{10}+774 q^9-1458 q^8-2435 q^7-1150 q^6+1296 q^5+2649 q^4+1503 q^3-1150 q^2-2744 q-1730+942 q^{-1} +2762 q^{-2} +1932 q^{-3} -798 q^{-4} -2730 q^{-5} -2016 q^{-6} +627 q^{-7} +2647 q^{-8} +2093 q^{-9} -474 q^{-10} -2542 q^{-11} -2118 q^{-12} +303 q^{-13} +2370 q^{-14} +2138 q^{-15} -92 q^{-16} -2159 q^{-17} -2122 q^{-18} -146 q^{-19} +1864 q^{-20} +2067 q^{-21} +410 q^{-22} -1501 q^{-23} -1946 q^{-24} -663 q^{-25} +1081 q^{-26} +1737 q^{-27} +859 q^{-28} -633 q^{-29} -1428 q^{-30} -974 q^{-31} +215 q^{-32} +1063 q^{-33} +946 q^{-34} +127 q^{-35} -658 q^{-36} -816 q^{-37} -339 q^{-38} +298 q^{-39} +586 q^{-40} +418 q^{-41} -20 q^{-42} -349 q^{-43} -360 q^{-44} -142 q^{-45} +125 q^{-46} +255 q^{-47} +190 q^{-48} +11 q^{-49} -125 q^{-50} -150 q^{-51} -88 q^{-52} +25 q^{-53} +101 q^{-54} +89 q^{-55} +18 q^{-56} -35 q^{-57} -60 q^{-58} -47 q^{-59} +9 q^{-60} +36 q^{-61} +29 q^{-62} +6 q^{-63} -8 q^{-64} -18 q^{-65} -14 q^{-66} +6 q^{-67} +9 q^{-68} +3 q^{-69} -5 q^{-72} +3 q^{-74} - q^{-75} </math> \|		coloured_jones_5 = <math>-2 q^{46}+5 q^{44}+5 q^{43}-5 q^{41}-22 q^{40}-17 q^{39}+15 q^{38}+45 q^{37}+49 q^{36}+12 q^{35}-76 q^{34}-134 q^{33}-71 q^{32}+90 q^{31}+239 q^{30}+211 q^{29}-37 q^{28}-358 q^{27}-443 q^{26}-104 q^{25}+444 q^{24}+713 q^{23}+383 q^{22}-417 q^{21}-1034 q^{20}-774 q^{19}+299 q^{18}+1271 q^{17}+1238 q^{16}-9 q^{15}-1457 q^{14}-1706 q^{13}-348 q^{12}+1497 q^{11}+2121 q^{10}+774 q^9-1458 q^8-2435 q^7-1150 q^6+1296 q^5+2649 q^4+1503 q^3-1150 q^2-2744 q-1730+942 q^{-1} +2762 q^{-2} +1932 q^{-3} -798 q^{-4} -2730 q^{-5} -2016 q^{-6} +627 q^{-7} +2647 q^{-8} +2093 q^{-9} -474 q^{-10} -2542 q^{-11} -2118 q^{-12} +303 q^{-13} +2370 q^{-14} +2138 q^{-15} -92 q^{-16} -2159 q^{-17} -2122 q^{-18} -146 q^{-19} +1864 q^{-20} +2067 q^{-21} +410 q^{-22} -1501 q^{-23} -1946 q^{-24} -663 q^{-25} +1081 q^{-26} +1737 q^{-27} +859 q^{-28} -633 q^{-29} -1428 q^{-30} -974 q^{-31} +215 q^{-32} +1063 q^{-33} +946 q^{-34} +127 q^{-35} -658 q^{-36} -816 q^{-37} -339 q^{-38} +298 q^{-39} +586 q^{-40} +418 q^{-41} -20 q^{-42} -349 q^{-43} -360 q^{-44} -142 q^{-45} +125 q^{-46} +255 q^{-47} +190 q^{-48} +11 q^{-49} -125 q^{-50} -150 q^{-51} -88 q^{-52} +25 q^{-53} +101 q^{-54} +89 q^{-55} +18 q^{-56} -35 q^{-57} -60 q^{-58} -47 q^{-59} +9 q^{-60} +36 q^{-61} +29 q^{-62} +6 q^{-63} -8 q^{-64} -18 q^{-65} -14 q^{-66} +6 q^{-67} +9 q^{-68} +3 q^{-69} -5 q^{-72} +3 q^{-74} - q^{-75} </math> \|
	coloured_jones_6 = <math>q^{68}-q^{67}-q^{66}-2 q^{63}-3 q^{62}+10 q^{61}+8 q^{60}+5 q^{59}+2 q^{58}-11 q^{57}-36 q^{56}-51 q^{55}+2 q^{54}+52 q^{53}+90 q^{52}+114 q^{51}+60 q^{50}-114 q^{49}-288 q^{48}-262 q^{47}-84 q^{46}+205 q^{45}+546 q^{44}+645 q^{43}+206 q^{42}-547 q^{41}-1049 q^{40}-1041 q^{39}-388 q^{38}+915 q^{37}+1991 q^{36}+1786 q^{35}+248 q^{34}-1692 q^{33}-2968 q^{32}-2693 q^{31}-157 q^{30}+3089 q^{29}+4578 q^{28}+3112 q^{27}-593 q^{26}-4539 q^{25}-6351 q^{24}-3522 q^{23}+2249 q^{22}+6962 q^{21}+7300 q^{20}+2819 q^{19}-4116 q^{18}-9482 q^{17}-8029 q^{16}-769 q^{15}+7388 q^{14}+10770 q^{13}+7097 q^{12}-1757 q^{11}-10661 q^{10}-11619 q^9-4382 q^8+6077 q^7+12288 q^6+10342 q^5+1019 q^4-10185 q^3-13327 q^2-7014 q+4337+12253 q^{-1} +11916 q^{-2} +3013 q^{-3} -9143 q^{-4} -13633 q^{-5} -8352 q^{-6} +2987 q^{-7} +11590 q^{-8} +12374 q^{-9} +4174 q^{-10} -8078 q^{-11} -13313 q^{-12} -8999 q^{-13} +1882 q^{-14} +10654 q^{-15} +12370 q^{-16} +5123 q^{-17} -6725 q^{-18} -12568 q^{-19} -9519 q^{-20} +396 q^{-21} +9107 q^{-22} +12003 q^{-23} +6335 q^{-24} -4511 q^{-25} -11000 q^{-26} -9870 q^{-27} -1796 q^{-28} +6409 q^{-29} +10771 q^{-30} +7563 q^{-31} -1310 q^{-32} -8082 q^{-33} -9319 q^{-34} -4130 q^{-35} +2602 q^{-36} +8045 q^{-37} +7763 q^{-38} +1982 q^{-39} -3984 q^{-40} -7074 q^{-41} -5221 q^{-42} -1130 q^{-43} +4071 q^{-44} +6014 q^{-45} +3720 q^{-46} -115 q^{-47} -3501 q^{-48} -4123 q^{-49} -3012 q^{-50} +447 q^{-51} +2891 q^{-52} +3087 q^{-53} +1745 q^{-54} -378 q^{-55} -1682 q^{-56} -2487 q^{-57} -1152 q^{-58} +302 q^{-59} +1223 q^{-60} +1377 q^{-61} +814 q^{-62} +165 q^{-63} -955 q^{-64} -843 q^{-65} -547 q^{-66} -48 q^{-67} +313 q^{-68} +497 q^{-69} +567 q^{-70} -28 q^{-71} -124 q^{-72} -285 q^{-73} -232 q^{-74} -181 q^{-75} +16 q^{-76} +262 q^{-77} +88 q^{-78} +123 q^{-79} - q^{-80} -38 q^{-81} -141 q^{-82} -96 q^{-83} +45 q^{-84} -2 q^{-85} +63 q^{-86} +39 q^{-87} +38 q^{-88} -36 q^{-89} -40 q^{-90} + q^{-91} -20 q^{-92} +9 q^{-93} +9 q^{-94} +23 q^{-95} -6 q^{-96} -9 q^{-97} +4 q^{-98} -7 q^{-99} +5 q^{-102} -3 q^{-104} + q^{-105} </math> \|		coloured_jones_6 = <math>q^{68}-q^{67}-q^{66}-2 q^{63}-3 q^{62}+10 q^{61}+8 q^{60}+5 q^{59}+2 q^{58}-11 q^{57}-36 q^{56}-51 q^{55}+2 q^{54}+52 q^{53}+90 q^{52}+114 q^{51}+60 q^{50}-114 q^{49}-288 q^{48}-262 q^{47}-84 q^{46}+205 q^{45}+546 q^{44}+645 q^{43}+206 q^{42}-547 q^{41}-1049 q^{40}-1041 q^{39}-388 q^{38}+915 q^{37}+1991 q^{36}+1786 q^{35}+248 q^{34}-1692 q^{33}-2968 q^{32}-2693 q^{31}-157 q^{30}+3089 q^{29}+4578 q^{28}+3112 q^{27}-593 q^{26}-4539 q^{25}-6351 q^{24}-3522 q^{23}+2249 q^{22}+6962 q^{21}+7300 q^{20}+2819 q^{19}-4116 q^{18}-9482 q^{17}-8029 q^{16}-769 q^{15}+7388 q^{14}+10770 q^{13}+7097 q^{12}-1757 q^{11}-10661 q^{10}-11619 q^9-4382 q^8+6077 q^7+12288 q^6+10342 q^5+1019 q^4-10185 q^3-13327 q^2-7014 q+4337+12253 q^{-1} +11916 q^{-2} +3013 q^{-3} -9143 q^{-4} -13633 q^{-5} -8352 q^{-6} +2987 q^{-7} +11590 q^{-8} +12374 q^{-9} +4174 q^{-10} -8078 q^{-11} -13313 q^{-12} -8999 q^{-13} +1882 q^{-14} +10654 q^{-15} +12370 q^{-16} +5123 q^{-17} -6725 q^{-18} -12568 q^{-19} -9519 q^{-20} +396 q^{-21} +9107 q^{-22} +12003 q^{-23} +6335 q^{-24} -4511 q^{-25} -11000 q^{-26} -9870 q^{-27} -1796 q^{-28} +6409 q^{-29} +10771 q^{-30} +7563 q^{-31} -1310 q^{-32} -8082 q^{-33} -9319 q^{-34} -4130 q^{-35} +2602 q^{-36} +8045 q^{-37} +7763 q^{-38} +1982 q^{-39} -3984 q^{-40} -7074 q^{-41} -5221 q^{-42} -1130 q^{-43} +4071 q^{-44} +6014 q^{-45} +3720 q^{-46} -115 q^{-47} -3501 q^{-48} -4123 q^{-49} -3012 q^{-50} +447 q^{-51} +2891 q^{-52} +3087 q^{-53} +1745 q^{-54} -378 q^{-55} -1682 q^{-56} -2487 q^{-57} -1152 q^{-58} +302 q^{-59} +1223 q^{-60} +1377 q^{-61} +814 q^{-62} +165 q^{-63} -955 q^{-64} -843 q^{-65} -547 q^{-66} -48 q^{-67} +313 q^{-68} +497 q^{-69} +567 q^{-70} -28 q^{-71} -124 q^{-72} -285 q^{-73} -232 q^{-74} -181 q^{-75} +16 q^{-76} +262 q^{-77} +88 q^{-78} +123 q^{-79} - q^{-80} -38 q^{-81} -141 q^{-82} -96 q^{-83} +45 q^{-84} -2 q^{-85} +63 q^{-86} +39 q^{-87} +38 q^{-88} -36 q^{-89} -40 q^{-90} + q^{-91} -20 q^{-92} +9 q^{-93} +9 q^{-94} +23 q^{-95} -6 q^{-96} -9 q^{-97} +4 q^{-98} -7 q^{-99} +5 q^{-102} -3 q^{-104} + q^{-105} </math> \|
	coloured_jones_7 = \|		coloured_jones_7 = <math>\textrm{NotAvailable}(q)</math> \|
	computer_talk =		computer_talk =
	<table>		<table>
Line 48:		Line 51:
	<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, 146]]</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, 146]]</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[5, 18, 6, 19], X[8, 3, 9, 4], X[2, 9, 3, 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[4, 2, 5, 1], X[5, 18, 6, 19], X[8, 3, 9, 4], X[2, 9, 3, 10],
Line 68:		Line 71:
	<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, 146]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_146_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, 146]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_146_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, 146]]&) /@ {~~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, 146]]&) /@ {
			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, 1, 2, 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, 1, 2, 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, 146]][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, 146]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:37, 30 August 2005

2005-08-30T14:37:59Z

Show changes

DrorsRobot at 01:05, 30 August 2005

2005-08-30T01:05:20Z

← Older revision		Revision as of 21:05, 29 August 2005
Line 1:		Line 1:
			<!-- This page was generated from the splice template "Rolfsen_Splice_Template". Please do not edit! -->
	<!-- -->		<!-- -->
	<!-- -->		<!-- -->
Line 200:		Line 201:
	</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 22:25, 29 August 2005

2005-08-29T22:25:53Z

Show changes

ScottTestRobot at 00:11, 29 August 2005

2005-08-29T00:11:16Z

← Older revision		Revision as of 20:11, 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=146\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-1,-2,7,-6,-3,4,8,-5,6,-9,10,-7,5,-8,2,-10,9/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=146\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-1,-2,7,-6,-3,4,8,-5,6,-9,10,-7,5,-8,2,-10,9/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=15.3846%><table cellpadding=0 cellspacing=0>		<td width=15.3846%><table cellpadding=0 cellspacing=0>
Line 46:		Line 39:
	<tr align=center><td>-9</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>2</td></tr>		<tr align=center><td>-9</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>2</td></tr>
	<tr align=center><td>-11</td><td bgcolor=yellow>1</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>-11</td><td bgcolor=yellow>1</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 130:		Line 122:
	q t</nowiki></pre></td></tr>		q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:47, 28 August 2005

2005-08-28T01:47:59Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:31Z

Resetting knot page to basic template.

New page

10 146 - Revision history

ScottTestRobot at 22:02, 1 September 2005

DrorsRobot at 22:47, 31 August 2005

ScottKnotPageRobot at 14:37, 30 August 2005

DrorsRobot at 01:05, 30 August 2005

DrorsRobot at 22:25, 29 August 2005

ScottTestRobot at 00:11, 29 August 2005

ScottTestRobot at 01:47, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.