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	<id>https://katlas.org/index.php?action=history&amp;feed=atom&amp;title=Data%3AL11n9%2FKauffman_Polynomial</id>
	<title>Data:L11n9/Kauffman Polynomial - Revision history</title>
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	<updated>2026-04-05T14:32:19Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://katlas.org/index.php?title=Data:L11n9/Kauffman_Polynomial&amp;diff=1715266&amp;oldid=prev</id>
		<title>ScottDataRobot at 20:36, 20 February 2013</title>
		<link rel="alternate" type="text/html" href="https://katlas.org/index.php?title=Data:L11n9/Kauffman_Polynomial&amp;diff=1715266&amp;oldid=prev"/>
		<updated>2013-02-20T20:36:46Z</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 16:36, 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;
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  &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;a^&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;9&lt;/del&gt;-a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; z^9-2 a^4 z&lt;/del&gt;^8&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-4 &lt;/del&gt;a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;8-2 z^8&lt;/del&gt;-a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/del&gt; z&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^7&lt;/del&gt;+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2 &lt;/del&gt;a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^3 z&lt;/del&gt;^7&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+2 a&lt;/del&gt; z&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^7-z^7 a&lt;/del&gt;^{-1} +&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;10 &lt;/del&gt;a^&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;6+20&lt;/del&gt; a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^2 z&lt;/del&gt;^6+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;10&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6+&lt;/del&gt;4 a^5 z^5+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;8&lt;/del&gt; a^&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;5+9&lt;/del&gt; a z&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^5&lt;/del&gt;+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/del&gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z&lt;/del&gt;^5 &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a&lt;/del&gt;^{-1} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/del&gt;a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/del&gt;-15 a^4 z^4-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;27&lt;/del&gt; a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4-13&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/del&gt;-a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7&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;6&lt;/del&gt; a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3-&lt;/del&gt;18 a^3 z^3-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;20&lt;/del&gt; a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; z&lt;/del&gt;^3&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-7&lt;/del&gt; z&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^&lt;/del&gt;3 a^{-1} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/del&gt;a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;8&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2+&lt;/del&gt;8 a^&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;2&lt;/del&gt;+12 a^2 z^2+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/del&gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z&lt;/del&gt;^2+a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^7&lt;/del&gt; z&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+6&lt;/del&gt; a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^5&lt;/del&gt; z+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;12&lt;/del&gt; a^&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;z+11&lt;/del&gt; a z&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+4&lt;/del&gt; z a^{-1} +a^&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;2&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;6-2&lt;/del&gt; a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^2-a^7 z&lt;/del&gt;^{-1} -&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/del&gt; a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^5&lt;/del&gt; z&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; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-3&lt;/del&gt; a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^3 z&lt;/del&gt;^{-1} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/del&gt;2 a z^{-1} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/del&gt; a^{-1} z^{-1} &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;
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  &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;a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;8&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt;-a^8&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7&lt;/ins&gt; z^&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;7&lt;/ins&gt; z+a^7 z^{-1} +a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4-2&lt;/ins&gt; a^6+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a^5&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7-&lt;/ins&gt;4 a^5 z^5+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3-6&lt;/ins&gt; a&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^5&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;a&lt;/ins&gt;^5 &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;+2 &lt;/ins&gt;a^&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;8&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;10 a^4 z^6+&lt;/ins&gt;15 a^4 z^4-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;8&lt;/ins&gt; a^&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;2+a^3&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;9&lt;/ins&gt;-&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;3&lt;/ins&gt; z^&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;8&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5+&lt;/ins&gt;18 a^3 z^3-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;12&lt;/ins&gt; a^3 z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;3 a&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^3 z&lt;/ins&gt;^{-1} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+4 &lt;/ins&gt;a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt; z^8&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-20&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/ins&gt;+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;27 a^2 z^4-&lt;/ins&gt;12 a^2 z^2+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a&lt;/ins&gt;^2+a z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^9-2&lt;/ins&gt; a z&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;z^7&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{-1}&lt;/ins&gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-9&lt;/ins&gt; a z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^5-5&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;20 &lt;/ins&gt;a&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;3&lt;/ins&gt;+&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;z&lt;/ins&gt;^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt; a^{-1} -&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;11&lt;/ins&gt; a z-&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;z&lt;/ins&gt; a^{-1} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;2 a z^{-1} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt; a^{-1} z^{-1} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+2 z^8-10 z^6+13 z^4-5 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:L11n9/Kauffman_Polynomial&amp;diff=81871&amp;oldid=prev</id>
		<title>ScottDataRobot at 19:35, 26 August 2005</title>
		<link rel="alternate" type="text/html" href="https://katlas.org/index.php?title=Data:L11n9/Kauffman_Polynomial&amp;diff=81871&amp;oldid=prev"/>
		<updated>2005-08-26T19:35:21Z</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;-a^3 z^9-a z^9-2 a^4 z^8-4 a^2 z^8-2 z^8-a^5 z^7+2 a^3 z^7+2 a z^7-z^7 a^{-1} +10 a^4 z^6+20 a^2 z^6+10 z^6+4 a^5 z^5+8 a^3 z^5+9 a z^5+5 z^5 a^{-1} -a^6 z^4-15 a^4 z^4-27 a^2 z^4-13 z^4-a^7 z^3-6 a^5 z^3-18 a^3 z^3-20 a z^3-7 z^3 a^{-1} -a^8 z^2+8 a^4 z^2+12 a^2 z^2+5 z^2+a^7 z+6 a^5 z+12 a^3 z+11 a z+4 z a^{-1} +a^8+2 a^6-2 a^2-a^7 z^{-1} -3 a^5 z^{-1} -3 a^3 z^{-1} -2 a z^{-1} - a^{-1} z^{-1} &amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>ScottDataRobot</name></author>
	</entry>
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