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	<id>https://katlas.org/index.php?action=history&amp;feed=atom&amp;title=Data%3AL11n146%2FKauffman_Polynomial</id>
	<title>Data:L11n146/Kauffman Polynomial - Revision history</title>
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	<updated>2026-06-21T20:16:15Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://katlas.org/index.php?title=Data:L11n146/Kauffman_Polynomial&amp;diff=1713819&amp;oldid=prev</id>
		<title>ScottDataRobot at 20:05, 20 February 2013</title>
		<link rel="alternate" type="text/html" href="https://katlas.org/index.php?title=Data:L11n146/Kauffman_Polynomial&amp;diff=1713819&amp;oldid=prev"/>
		<updated>2013-02-20T20:05:39Z</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 16:05, 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;-a &lt;/del&gt;z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;9-z^9&lt;/del&gt; a^{-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/del&gt;} -3 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&lt;/del&gt; z^&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;2&lt;/del&gt;} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-5 z^8-3&lt;/del&gt; a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3 z^7-&lt;/del&gt;4&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; a&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7&lt;/del&gt;-2 z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7&lt;/del&gt; a^{-&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;z^7&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;-a^4 z^6&lt;/del&gt;+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7&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;6&lt;/del&gt;+&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;6&lt;/del&gt; a^{-&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;+11 z^6+&lt;/del&gt;10 a^3 z^5+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;19 a z^5+7&lt;/del&gt; z^5 a^{-&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;-2&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/del&gt; a^{-3} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/del&gt;3 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;4&lt;/del&gt;-&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;4&lt;/del&gt; a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{-&lt;/del&gt;2&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;-4&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;4&lt;/del&gt;} -&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4 z^4-9&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;3&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;18 a 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;3&lt;/del&gt; a^{-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/del&gt;} +z^&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&lt;/del&gt;} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-z^&lt;/del&gt;3 a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{-5} -&lt;/del&gt;2&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; a^4&lt;/del&gt; z^2-3 a^2 z^&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;2 &lt;/del&gt;z^&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;4&lt;/del&gt;} &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;2&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&lt;/del&gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z+8&lt;/del&gt; a z&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/del&gt;5 z a^{-1} +3 a^{-&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;+&lt;/del&gt; a^{-&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;3-&lt;/del&gt;2 a z^{-1} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/del&gt;3 a^{-1} z^{-1} &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;a&lt;/del&gt;^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{&lt;/del&gt;-3&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;}&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;&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;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;5&lt;/ins&gt;} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+a^4 z^6&lt;/ins&gt;-3 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;4+4&lt;/ins&gt; z^&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;4&lt;/ins&gt;} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+2&lt;/ins&gt; a^4 z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt;-2 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;} - a^{-&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; 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;+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;3&lt;/ins&gt;} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/ins&gt;10 a^3 z^5+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt; z^5 a^{-&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;+9 a^3&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3-z^3&lt;/ins&gt; a^{-3} &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&lt;/ins&gt; z&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;{&lt;/ins&gt;-&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;{-1} +3&lt;/ins&gt; a^2 &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z^8+2&lt;/ins&gt; z^&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;2&lt;/ins&gt;} -&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;2&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/ins&gt;-3 z^&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;2&lt;/ins&gt;} +&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;4&lt;/ins&gt; a^{-&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;+&lt;/ins&gt;3 a^2 z^2-3 a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{-&lt;/ins&gt;2&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;} +a&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;9&lt;/ins&gt;+z^&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;1&lt;/ins&gt;} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+4 a&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;2 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;-19&lt;/ins&gt; a z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^&lt;/ins&gt;5&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;^5&lt;/ins&gt; a^{-1} +&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;18 a z^3+7 z^&lt;/ins&gt;3 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;-8 a z-5 z&lt;/ins&gt; a^{-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/ins&gt;} +2 a z^{-1} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;3 a^{-1} z^{-1} &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;z&lt;/ins&gt;^&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;11 z^6+4 z^4+&lt;/ins&gt;3 z^&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;3&lt;/ins&gt;&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>ScottDataRobot</name></author>
	</entry>
	<entry>
		<id>https://katlas.org/index.php?title=Data:L11n146/Kauffman_Polynomial&amp;diff=90257&amp;oldid=prev</id>
		<title>ScottDataRobot at 02:49, 27 August 2005</title>
		<link rel="alternate" type="text/html" href="https://katlas.org/index.php?title=Data:L11n146/Kauffman_Polynomial&amp;diff=90257&amp;oldid=prev"/>
		<updated>2005-08-27T02:49:29Z</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 z^9-z^9 a^{-1} -3 a^2 z^8-2 z^8 a^{-2} -5 z^8-3 a^3 z^7-4 a z^7-2 z^7 a^{-1} -z^7 a^{-3} -a^4 z^6+7 a^2 z^6+3 z^6 a^{-2} +11 z^6+10 a^3 z^5+19 a z^5+7 z^5 a^{-1} -2 z^5 a^{-3} +3 a^4 z^4-5 z^4 a^{-2} -4 z^4 a^{-4} -4 z^4-9 a^3 z^3-18 a z^3-7 z^3 a^{-1} +z^3 a^{-3} -z^3 a^{-5} -2 a^4 z^2-3 a^2 z^2+2 z^2 a^{-4} -3 z^2+3 a^3 z+8 a z+5 z a^{-1} +3 a^{-2} + a^{-4} +3-2 a z^{-1} -3 a^{-1} z^{-1} - a^{-3} z^{-1} &amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>ScottDataRobot</name></author>
	</entry>
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