ScottTestRobot at 22:04, 1 September 2005

2005-09-01T22:04:13Z

DrorsRobot at 22:52, 31 August 2005

2005-08-31T22:52:10Z

← Older revision		Revision as of 18:52, 31 August 2005
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	coloured_jones_5 = <math>q^{100}-2 q^{99}+q^{98}+q^{95}-q^{94}-2 q^{93}+2 q^{92}+q^{91}-2 q^{90}+2 q^{89}+q^{88}-3 q^{87}-3 q^{85}-3 q^{84}+11 q^{83}+13 q^{82}-6 q^{81}-21 q^{80}-19 q^{79}+7 q^{78}+42 q^{77}+36 q^{76}-21 q^{75}-73 q^{74}-52 q^{73}+36 q^{72}+112 q^{71}+80 q^{70}-52 q^{69}-165 q^{68}-119 q^{67}+66 q^{66}+222 q^{65}+173 q^{64}-67 q^{63}-277 q^{62}-241 q^{61}+45 q^{60}+325 q^{59}+309 q^{58}-6 q^{57}-339 q^{56}-369 q^{55}-48 q^{54}+324 q^{53}+401 q^{52}+105 q^{51}-286 q^{50}-400 q^{49}-142 q^{48}+228 q^{47}+368 q^{46}+166 q^{45}-177 q^{44}-326 q^{43}-160 q^{42}+138 q^{41}+278 q^{40}+148 q^{39}-111 q^{38}-244 q^{37}-136 q^{36}+94 q^{35}+223 q^{34}+129 q^{33}-78 q^{32}-201 q^{31}-138 q^{30}+49 q^{29}+191 q^{28}+144 q^{27}-17 q^{26}-158 q^{25}-158 q^{24}-26 q^{23}+125 q^{22}+156 q^{21}+66 q^{20}-75 q^{19}-142 q^{18}-100 q^{17}+22 q^{16}+113 q^{15}+116 q^{14}+29 q^{13}-68 q^{12}-113 q^{11}-72 q^{10}+17 q^9+91 q^8+94 q^7+32 q^6-48 q^5-95 q^4-69 q^3+5 q^2+69 q+83+42 q^{-1} -33 q^{-2} -74 q^{-3} -63 q^{-4} -13 q^{-5} +42 q^{-6} +71 q^{-7} +40 q^{-8} -10 q^{-9} -42 q^{-10} -52 q^{-11} -30 q^{-12} +19 q^{-13} +41 q^{-14} +33 q^{-15} +19 q^{-16} -12 q^{-17} -39 q^{-18} -28 q^{-19} -6 q^{-20} +9 q^{-21} +30 q^{-22} +27 q^{-23} +3 q^{-24} -14 q^{-25} -21 q^{-26} -22 q^{-27} +15 q^{-29} +17 q^{-30} +12 q^{-31} -16 q^{-33} -11 q^{-34} -4 q^{-35} +2 q^{-36} +9 q^{-37} +9 q^{-38} -2 q^{-39} -3 q^{-40} -3 q^{-41} -4 q^{-42} +4 q^{-44} + q^{-45} - q^{-48} - q^{-49} + q^{-50} </math> \|		coloured_jones_5 = <math>q^{100}-2 q^{99}+q^{98}+q^{95}-q^{94}-2 q^{93}+2 q^{92}+q^{91}-2 q^{90}+2 q^{89}+q^{88}-3 q^{87}-3 q^{85}-3 q^{84}+11 q^{83}+13 q^{82}-6 q^{81}-21 q^{80}-19 q^{79}+7 q^{78}+42 q^{77}+36 q^{76}-21 q^{75}-73 q^{74}-52 q^{73}+36 q^{72}+112 q^{71}+80 q^{70}-52 q^{69}-165 q^{68}-119 q^{67}+66 q^{66}+222 q^{65}+173 q^{64}-67 q^{63}-277 q^{62}-241 q^{61}+45 q^{60}+325 q^{59}+309 q^{58}-6 q^{57}-339 q^{56}-369 q^{55}-48 q^{54}+324 q^{53}+401 q^{52}+105 q^{51}-286 q^{50}-400 q^{49}-142 q^{48}+228 q^{47}+368 q^{46}+166 q^{45}-177 q^{44}-326 q^{43}-160 q^{42}+138 q^{41}+278 q^{40}+148 q^{39}-111 q^{38}-244 q^{37}-136 q^{36}+94 q^{35}+223 q^{34}+129 q^{33}-78 q^{32}-201 q^{31}-138 q^{30}+49 q^{29}+191 q^{28}+144 q^{27}-17 q^{26}-158 q^{25}-158 q^{24}-26 q^{23}+125 q^{22}+156 q^{21}+66 q^{20}-75 q^{19}-142 q^{18}-100 q^{17}+22 q^{16}+113 q^{15}+116 q^{14}+29 q^{13}-68 q^{12}-113 q^{11}-72 q^{10}+17 q^9+91 q^8+94 q^7+32 q^6-48 q^5-95 q^4-69 q^3+5 q^2+69 q+83+42 q^{-1} -33 q^{-2} -74 q^{-3} -63 q^{-4} -13 q^{-5} +42 q^{-6} +71 q^{-7} +40 q^{-8} -10 q^{-9} -42 q^{-10} -52 q^{-11} -30 q^{-12} +19 q^{-13} +41 q^{-14} +33 q^{-15} +19 q^{-16} -12 q^{-17} -39 q^{-18} -28 q^{-19} -6 q^{-20} +9 q^{-21} +30 q^{-22} +27 q^{-23} +3 q^{-24} -14 q^{-25} -21 q^{-26} -22 q^{-27} +15 q^{-29} +17 q^{-30} +12 q^{-31} -16 q^{-33} -11 q^{-34} -4 q^{-35} +2 q^{-36} +9 q^{-37} +9 q^{-38} -2 q^{-39} -3 q^{-40} -3 q^{-41} -4 q^{-42} +4 q^{-44} + q^{-45} - q^{-48} - q^{-49} + q^{-50} </math> \|
	coloured_jones_6 = <math>q^{138}-2 q^{137}+q^{136}+q^{133}-3 q^{132}+4 q^{131}-4 q^{130}+3 q^{129}-2 q^{128}+6 q^{126}-8 q^{125}+5 q^{124}-8 q^{123}+5 q^{122}-2 q^{121}+7 q^{120}+16 q^{119}-22 q^{118}-6 q^{117}-14 q^{116}+15 q^{115}+11 q^{114}+25 q^{113}+17 q^{112}-64 q^{111}-35 q^{110}-5 q^{109}+64 q^{108}+55 q^{107}+35 q^{106}-31 q^{105}-165 q^{104}-76 q^{103}+60 q^{102}+197 q^{101}+151 q^{100}+10 q^{99}-178 q^{98}-368 q^{97}-143 q^{96}+203 q^{95}+463 q^{94}+355 q^{93}-9 q^{92}-428 q^{91}-728 q^{90}-331 q^{89}+330 q^{88}+840 q^{87}+739 q^{86}+135 q^{85}-629 q^{84}-1192 q^{83}-730 q^{82}+232 q^{81}+1114 q^{80}+1205 q^{79}+526 q^{78}-537 q^{77}-1478 q^{76}-1176 q^{75}-139 q^{74}+1024 q^{73}+1417 q^{72}+922 q^{71}-169 q^{70}-1348 q^{69}-1309 q^{68}-475 q^{67}+672 q^{66}+1211 q^{65}+990 q^{64}+126 q^{63}-996 q^{62}-1084 q^{61}-516 q^{60}+420 q^{59}+881 q^{58}+801 q^{57}+171 q^{56}-769 q^{55}-841 q^{54}-417 q^{53}+355 q^{52}+718 q^{51}+681 q^{50}+170 q^{49}-677 q^{48}-773 q^{47}-444 q^{46}+266 q^{45}+649 q^{44}+716 q^{43}+307 q^{42}-516 q^{41}-740 q^{40}-589 q^{39}+32 q^{38}+483 q^{37}+740 q^{36}+520 q^{35}-220 q^{34}-578 q^{33}-681 q^{32}-258 q^{31}+184 q^{30}+612 q^{29}+653 q^{28}+119 q^{27}-268 q^{26}-601 q^{25}-455 q^{24}-162 q^{23}+315 q^{22}+594 q^{21}+363 q^{20}+100 q^{19}-328 q^{18}-438 q^{17}-406 q^{16}-59 q^{15}+318 q^{14}+373 q^{13}+355 q^{12}+33 q^{11}-180 q^{10}-389 q^9-311 q^8-45 q^7+126 q^6+326 q^5+247 q^4+151 q^3-111 q^2-260 q-231-167 q^{-1} +57 q^{-2} +150 q^{-3} +265 q^{-4} +165 q^{-5} +3 q^{-6} -104 q^{-7} -216 q^{-8} -153 q^{-9} -104 q^{-10} +87 q^{-11} +169 q^{-12} +150 q^{-13} +115 q^{-14} -25 q^{-15} -87 q^{-16} -184 q^{-17} -102 q^{-18} -16 q^{-19} +43 q^{-20} +129 q^{-21} +102 q^{-22} +83 q^{-23} -48 q^{-24} -68 q^{-25} -84 q^{-26} -89 q^{-27} -8 q^{-28} +29 q^{-29} +95 q^{-30} +44 q^{-31} +47 q^{-32} +4 q^{-33} -56 q^{-34} -52 q^{-35} -53 q^{-36} +4 q^{-37} -5 q^{-38} +48 q^{-39} +49 q^{-40} +19 q^{-41} +2 q^{-42} -26 q^{-43} -17 q^{-44} -45 q^{-45} -4 q^{-46} +12 q^{-47} +18 q^{-48} +20 q^{-49} +11 q^{-50} +11 q^{-51} -23 q^{-52} -11 q^{-53} -9 q^{-54} -3 q^{-55} +2 q^{-56} +7 q^{-57} +14 q^{-58} -3 q^{-59} -3 q^{-61} -3 q^{-62} -4 q^{-63} - q^{-64} +5 q^{-65} + q^{-67} - q^{-70} - q^{-71} + q^{-72} </math> \|		coloured_jones_6 = <math>q^{138}-2 q^{137}+q^{136}+q^{133}-3 q^{132}+4 q^{131}-4 q^{130}+3 q^{129}-2 q^{128}+6 q^{126}-8 q^{125}+5 q^{124}-8 q^{123}+5 q^{122}-2 q^{121}+7 q^{120}+16 q^{119}-22 q^{118}-6 q^{117}-14 q^{116}+15 q^{115}+11 q^{114}+25 q^{113}+17 q^{112}-64 q^{111}-35 q^{110}-5 q^{109}+64 q^{108}+55 q^{107}+35 q^{106}-31 q^{105}-165 q^{104}-76 q^{103}+60 q^{102}+197 q^{101}+151 q^{100}+10 q^{99}-178 q^{98}-368 q^{97}-143 q^{96}+203 q^{95}+463 q^{94}+355 q^{93}-9 q^{92}-428 q^{91}-728 q^{90}-331 q^{89}+330 q^{88}+840 q^{87}+739 q^{86}+135 q^{85}-629 q^{84}-1192 q^{83}-730 q^{82}+232 q^{81}+1114 q^{80}+1205 q^{79}+526 q^{78}-537 q^{77}-1478 q^{76}-1176 q^{75}-139 q^{74}+1024 q^{73}+1417 q^{72}+922 q^{71}-169 q^{70}-1348 q^{69}-1309 q^{68}-475 q^{67}+672 q^{66}+1211 q^{65}+990 q^{64}+126 q^{63}-996 q^{62}-1084 q^{61}-516 q^{60}+420 q^{59}+881 q^{58}+801 q^{57}+171 q^{56}-769 q^{55}-841 q^{54}-417 q^{53}+355 q^{52}+718 q^{51}+681 q^{50}+170 q^{49}-677 q^{48}-773 q^{47}-444 q^{46}+266 q^{45}+649 q^{44}+716 q^{43}+307 q^{42}-516 q^{41}-740 q^{40}-589 q^{39}+32 q^{38}+483 q^{37}+740 q^{36}+520 q^{35}-220 q^{34}-578 q^{33}-681 q^{32}-258 q^{31}+184 q^{30}+612 q^{29}+653 q^{28}+119 q^{27}-268 q^{26}-601 q^{25}-455 q^{24}-162 q^{23}+315 q^{22}+594 q^{21}+363 q^{20}+100 q^{19}-328 q^{18}-438 q^{17}-406 q^{16}-59 q^{15}+318 q^{14}+373 q^{13}+355 q^{12}+33 q^{11}-180 q^{10}-389 q^9-311 q^8-45 q^7+126 q^6+326 q^5+247 q^4+151 q^3-111 q^2-260 q-231-167 q^{-1} +57 q^{-2} +150 q^{-3} +265 q^{-4} +165 q^{-5} +3 q^{-6} -104 q^{-7} -216 q^{-8} -153 q^{-9} -104 q^{-10} +87 q^{-11} +169 q^{-12} +150 q^{-13} +115 q^{-14} -25 q^{-15} -87 q^{-16} -184 q^{-17} -102 q^{-18} -16 q^{-19} +43 q^{-20} +129 q^{-21} +102 q^{-22} +83 q^{-23} -48 q^{-24} -68 q^{-25} -84 q^{-26} -89 q^{-27} -8 q^{-28} +29 q^{-29} +95 q^{-30} +44 q^{-31} +47 q^{-32} +4 q^{-33} -56 q^{-34} -52 q^{-35} -53 q^{-36} +4 q^{-37} -5 q^{-38} +48 q^{-39} +49 q^{-40} +19 q^{-41} +2 q^{-42} -26 q^{-43} -17 q^{-44} -45 q^{-45} -4 q^{-46} +12 q^{-47} +18 q^{-48} +20 q^{-49} +11 q^{-50} +11 q^{-51} -23 q^{-52} -11 q^{-53} -9 q^{-54} -3 q^{-55} +2 q^{-56} +7 q^{-57} +14 q^{-58} -3 q^{-59} -3 q^{-61} -3 q^{-62} -4 q^{-63} - q^{-64} +5 q^{-65} + q^{-67} - q^{-70} - q^{-71} + q^{-72} </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, 61]]</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, 61]]</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[8, 2, 9, 1], X[10, 4, 11, 3], X[2, 10, 3, 9], X[18, 12, 19, 11],		<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[8, 2, 9, 1], X[10, 4, 11, 3], X[2, 10, 3, 9], X[18, 12, 19, 11],
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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, 61]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_61_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, 61]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_61_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, 61]]&) /@ {~~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, 61]]&) /@ {
			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, 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, {2, 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, 61]][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, 61]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:40, 30 August 2005

2005-08-30T14:40:18Z

Show changes

DrorsRobot at 01:07, 30 August 2005

2005-08-30T01:07:58Z

← Older revision		Revision as of 21:07, 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 22:18, 29 August 2005

2005-08-29T22:18:06Z

Show changes

ScottTestRobot at 00:14, 29 August 2005

2005-08-29T00:14:14Z

← Older revision		Revision as of 20:14, 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=61\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-3,2,-8,6,-7,5,-1,3,-2,4,-10,9,-5,7,-6,8,-4,10,-9/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=61\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-3,2,-8,6,-7,5,-1,3,-2,4,-10,9,-5,7,-6,8,-4,10,-9/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>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>		<tr align=center><td>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
	<tr align=center><td>-5</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>-5</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 + q t</nowiki></pre></td></tr>		q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:50, 28 August 2005

2005-08-28T01:50:41Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:50:13Z

Resetting knot page to basic template.

New page

10 61 - Revision history

ScottTestRobot at 22:04, 1 September 2005

DrorsRobot at 22:52, 31 August 2005

ScottKnotPageRobot at 14:40, 30 August 2005

DrorsRobot at 01:07, 30 August 2005

DrorsRobot at 22:18, 29 August 2005

ScottTestRobot at 00:14, 29 August 2005

ScottTestRobot at 01:50, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.