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	<id>https://katlas.org/index.php?action=history&amp;feed=atom&amp;title=Data%3AL11a172%2FKauffman_Polynomial</id>
	<title>Data:L11a172/Kauffman Polynomial - Revision history</title>
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	<updated>2026-04-05T08:28:22Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://katlas.org/index.php?title=Data:L11a172/Kauffman_Polynomial&amp;diff=1718394&amp;oldid=prev</id>
		<title>ScottDataRobot at 21:42, 20 February 2013</title>
		<link rel="alternate" type="text/html" href="https://katlas.org/index.php?title=Data:L11a172/Kauffman_Polynomial&amp;diff=1718394&amp;oldid=prev"/>
		<updated>2013-02-20T21:42:52Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 17:42, 20 February 2013&lt;/td&gt;
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  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
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  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/del&gt;z^4&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/del&gt;a^{10}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/del&gt;z^2 a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{10}-3&lt;/del&gt; z^5 a^9&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+3&lt;/del&gt; z^3 a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;9-5&lt;/del&gt; z^6 a^8&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+5&lt;/del&gt; z^4&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/del&gt;a^8&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/del&gt;z^2 a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;8-&lt;/del&gt;7 z^7 a^7&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+12&lt;/del&gt; z^5 a^7&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-10&lt;/del&gt; z^3 a^7&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+2&lt;/del&gt; z a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7-7&lt;/del&gt; z^8 a^6&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+14&lt;/del&gt; z^6 a^6&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-12&lt;/del&gt; z^4 a^6&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+2&lt;/del&gt; z^2 a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6-&lt;/del&gt;5 z^9 a^5&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+9&lt;/del&gt; z^7 a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5-&lt;/del&gt;5 z^5 a^5&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+2&lt;/del&gt; z^3 a^5&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-2&lt;/del&gt; z a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5-2&lt;/del&gt; z^{10} a^4&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-2&lt;/del&gt; z^8 a^4&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+16&lt;/del&gt; z^6 a^4&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-16&lt;/del&gt; z^4 a^4&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+6&lt;/del&gt; z^2 a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4-9&lt;/del&gt; z^9 a^3&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+33&lt;/del&gt; z^7 a^3&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-46&lt;/del&gt; z^5 a^3&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+36&lt;/del&gt; z^3 a^3&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-11&lt;/del&gt; z&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; a^3+&lt;/del&gt;a^3 z^{-1} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/del&gt;2 z^{10} a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2+&lt;/del&gt;2 z^8 a^2&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+9&lt;/del&gt; z^6 a^2&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-11&lt;/del&gt; z^4 a^2&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+5&lt;/del&gt; z^2&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/del&gt;a^2&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-a^2-&lt;/del&gt;4 z^9 a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+16&lt;/del&gt; z^7 a-22&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; z^5&lt;/del&gt; a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+17&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3 a&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7&lt;/del&gt; z a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+a z&lt;/del&gt;^{-1} -&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;8&lt;/del&gt;+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;12&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6-13 z^4+&lt;/del&gt;3&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; z^2-z^7&lt;/del&gt; a^{-1} +&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/del&gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z^5&lt;/del&gt; a^{-1} -&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/del&gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a&lt;/del&gt;^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1}&lt;/del&gt; &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a^{10} &lt;/ins&gt;z^4&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/ins&gt;a^{10}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/ins&gt;z^2&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+3&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;9&lt;/ins&gt; z^5&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-3&lt;/ins&gt; a^9 z^3&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+5&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;8&lt;/ins&gt; z^6&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-5&lt;/ins&gt; a^8 z^4&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;a^8&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/ins&gt;z^2&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+7&lt;/ins&gt; a^7 z^7&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-12&lt;/ins&gt; a^7 z^5&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+10&lt;/ins&gt; a^7 z^3&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-2&lt;/ins&gt; a^7 z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+7&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/ins&gt; z^8&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-14&lt;/ins&gt; a^6 z^6&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+12&lt;/ins&gt; a^6 z^4&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-2&lt;/ins&gt; a^6 z^2&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+5&lt;/ins&gt; a^5 z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;9-&lt;/ins&gt;9 a^5 z^7&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+5&lt;/ins&gt; a^5 z^5&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-2&lt;/ins&gt; a^5 z^3&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+2&lt;/ins&gt; a^5 z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+2&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/ins&gt; z^{10}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+2&lt;/ins&gt; a^4 z^8&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-16&lt;/ins&gt; a^4 z^6&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+16&lt;/ins&gt; a^4 z^4&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-6&lt;/ins&gt; a^4 z^2&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+9&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt; z^9&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-33&lt;/ins&gt; a^3 z^7&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+46&lt;/ins&gt; a^3 z^5&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-36&lt;/ins&gt; a^3 z^3&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+11&lt;/ins&gt; a^3 z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/ins&gt;a^3 z^{-1} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+2 a^&lt;/ins&gt;2 z^{10}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-2&lt;/ins&gt; a^2 z^8&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-9&lt;/ins&gt; a^2 z^6&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+11&lt;/ins&gt; a^2 z^4&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-5&lt;/ins&gt; a^2 z^2&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;a^2&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;4&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; a&lt;/ins&gt; z^9&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-16&lt;/ins&gt; a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z^7+&lt;/ins&gt;z^7 a&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^{&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1} +&lt;/ins&gt;22 a z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/ins&gt; z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^5&lt;/ins&gt; a^{-1} -&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;17 a&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt;+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/ins&gt; z^3 a^{-1} +&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7&lt;/ins&gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a&lt;/ins&gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z-&lt;/ins&gt;a&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; z&lt;/ins&gt;^{-1} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+3 z^8&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;12&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6+13&lt;/ins&gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z&lt;/ins&gt;^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z^2&lt;/ins&gt;&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;
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		<author><name>ScottDataRobot</name></author>
	</entry>
	<entry>
		<id>https://katlas.org/index.php?title=Data:L11a172/Kauffman_Polynomial&amp;diff=88106&amp;oldid=prev</id>
		<title>ScottDataRobot at 00:59, 27 August 2005</title>
		<link rel="alternate" type="text/html" href="https://katlas.org/index.php?title=Data:L11a172/Kauffman_Polynomial&amp;diff=88106&amp;oldid=prev"/>
		<updated>2005-08-27T00:59:48Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;lt;math&amp;gt;-z^4 a^{10}+z^2 a^{10}-3 z^5 a^9+3 z^3 a^9-5 z^6 a^8+5 z^4 a^8-z^2 a^8-7 z^7 a^7+12 z^5 a^7-10 z^3 a^7+2 z a^7-7 z^8 a^6+14 z^6 a^6-12 z^4 a^6+2 z^2 a^6-5 z^9 a^5+9 z^7 a^5-5 z^5 a^5+2 z^3 a^5-2 z a^5-2 z^{10} a^4-2 z^8 a^4+16 z^6 a^4-16 z^4 a^4+6 z^2 a^4-9 z^9 a^3+33 z^7 a^3-46 z^5 a^3+36 z^3 a^3-11 z a^3+a^3 z^{-1} -2 z^{10} a^2+2 z^8 a^2+9 z^6 a^2-11 z^4 a^2+5 z^2 a^2-a^2-4 z^9 a+16 z^7 a-22 z^5 a+17 z^3 a-7 z a+a z^{-1} -3 z^8+12 z^6-13 z^4+3 z^2-z^7 a^{-1} +4 z^5 a^{-1} -4 z^3 a^{-1} &amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>ScottDataRobot</name></author>
	</entry>
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