https://katlas.org/index.php?action=history&feed=atom&title=Data%3AL11a449%2FKauffman_Polynomial 2026-05-21T17:44:28Z Revision history for this page on the wiki MediaWiki 1.39.6 https://katlas.org/index.php?title=Data:L11a449/Kauffman_Polynomial&diff=1716392&oldid=prev 2013-02-20T21:00:27Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:00, 20 February 2013</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="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;"><div>&lt;math&gt;a^<del style="font-weight: bold; text-decoration: none;">2</del> z^<del style="font-weight: bold; text-decoration: none;">{10}+z^{10}+</del>3 a^<del style="font-weight: bold; text-decoration: none;">3</del> z^<del style="font-weight: bold; text-decoration: none;">9</del>+<del style="font-weight: bold; text-decoration: none;">7</del> a<del style="font-weight: bold; text-decoration: none;"> z</del>^<del style="font-weight: bold; text-decoration: none;">9+4</del> z^<del style="font-weight: bold; text-decoration: none;">9 </del>a^<del style="font-weight: bold; text-decoration: none;">{-1} </del>+<del style="font-weight: bold; text-decoration: none;">4</del> a^<del style="font-weight: bold; text-decoration: none;">4</del> z^<del style="font-weight: bold; text-decoration: none;">8+</del>8 a^<del style="font-weight: bold; text-decoration: none;">2</del> z^<del style="font-weight: bold; text-decoration: none;">8</del>+<del style="font-weight: bold; text-decoration: none;">6 </del>z^<del style="font-weight: bold; text-decoration: none;">8</del> a^{-<del style="font-weight: bold; text-decoration: none;">2</del>} +<del style="font-weight: bold; text-decoration: none;">10 z^8+3</del> a^5 z<del style="font-weight: bold; text-decoration: none;">^7-a</del>^3<del style="font-weight: bold; text-decoration: none;"> z^7</del>-<del style="font-weight: bold; text-decoration: none;">14 a</del> z^<del style="font-weight: bold; text-decoration: none;">7-5 z^7</del> a^{-<del style="font-weight: bold; text-decoration: none;">1</del>} <del style="font-weight: bold; text-decoration: none;">+5 z^7 a^{</del>-<del style="font-weight: bold; text-decoration: none;">3} +</del>a^<del style="font-weight: bold; text-decoration: none;">6</del> z<del style="font-weight: bold; text-decoration: none;">^6-8</del> a^4 z^<del style="font-weight: bold; text-decoration: none;">6</del>-<del style="font-weight: bold; text-decoration: none;">30</del> a^<del style="font-weight: bold; text-decoration: none;">2</del> z^6<del style="font-weight: bold; text-decoration: none;">-16</del> z^6 a^{-<del style="font-weight: bold; text-decoration: none;">2</del>} +<del style="font-weight: bold; text-decoration: none;">3</del> z^6 a^{-4} -<del style="font-weight: bold; text-decoration: none;">40</del> z^<del style="font-weight: bold; text-decoration: none;">6</del>-<del style="font-weight: bold; text-decoration: none;">8</del> a^<del style="font-weight: bold; text-decoration: none;">5</del> z^<del style="font-weight: bold; text-decoration: none;">5</del>-<del style="font-weight: bold; text-decoration: none;">13</del> <del style="font-weight: bold; text-decoration: none;">a^</del>3 <del style="font-weight: bold; text-decoration: none;">z</del>^<del style="font-weight: bold; text-decoration: none;">5</del>+3 a z^<del style="font-weight: bold; text-decoration: none;">5</del>-<del style="font-weight: bold; text-decoration: none;">4</del> z^5 a^{-<del style="font-weight: bold; text-decoration: none;">1</del>} -<del style="font-weight: bold; text-decoration: none;">11</del> <del style="font-weight: bold; text-decoration: none;">z</del>^<del style="font-weight: bold; text-decoration: none;">5</del> <del style="font-weight: bold; text-decoration: none;">a</del>^<del style="font-weight: bold; text-decoration: none;">{</del>-<del style="font-weight: bold; text-decoration: none;">3}</del> <del style="font-weight: bold; text-decoration: none;">+</del>z^5 a^{-<del style="font-weight: bold; text-decoration: none;">5</del>} <del style="font-weight: bold; text-decoration: none;">-3 a^6 z^4</del>+<del style="font-weight: bold; text-decoration: none;">a^4 z^4+39</del> a^<del style="font-weight: bold; text-decoration: none;">2</del> z^<del style="font-weight: bold; text-decoration: none;">4</del>+<del style="font-weight: bold; text-decoration: none;">21</del> z^<del style="font-weight: bold; text-decoration: none;">4</del> a^{-<del style="font-weight: bold; text-decoration: none;">2</del>} -<del style="font-weight: bold; text-decoration: none;">6</del> <del style="font-weight: bold; text-decoration: none;">z</del>^<del style="font-weight: bold; text-decoration: none;">4</del> a^{-<del style="font-weight: bold; text-decoration: none;">4</del>} +<del style="font-weight: bold; text-decoration: none;">62 z^4+5</del> a^<del style="font-weight: bold; text-decoration: none;">5</del> z^<del style="font-weight: bold; text-decoration: none;">3+14</del> a^<del style="font-weight: bold; text-decoration: none;">3</del> z^<del style="font-weight: bold; text-decoration: none;">3</del>+<del style="font-weight: bold; text-decoration: none;">16</del> a z^<del style="font-weight: bold; text-decoration: none;">3</del>+<del style="font-weight: bold; text-decoration: none;">16</del> z^<del style="font-weight: bold; text-decoration: none;">3</del> a^{-<del style="font-weight: bold; text-decoration: none;">1</del>} <del style="font-weight: bold; text-decoration: none;">+7</del> <del style="font-weight: bold; text-decoration: none;">z</del>^<del style="font-weight: bold; text-decoration: none;">3</del> <del style="font-weight: bold; text-decoration: none;">a</del>^<del style="font-weight: bold; text-decoration: none;">{</del>-<del style="font-weight: bold; text-decoration: none;">3} -2</del> z^<del style="font-weight: bold; text-decoration: none;">3</del> a^{-<del style="font-weight: bold; text-decoration: none;">5</del>} +<del style="font-weight: bold; text-decoration: none;">3</del> a^<del style="font-weight: bold; text-decoration: none;">6</del> z^<del style="font-weight: bold; text-decoration: none;">2-2</del> <del style="font-weight: bold; text-decoration: none;">a</del>^4 <del style="font-weight: bold; text-decoration: none;">z</del>^2-28 a^2 z^2-13 z^2 a^{-2} <del style="font-weight: bold; text-decoration: none;">+z^</del>2 a^{-<del style="font-weight: bold; text-decoration: none;">4</del>} <del style="font-weight: bold; text-decoration: none;">-37</del> <del style="font-weight: bold; text-decoration: none;">z</del>^2-a^<del style="font-weight: bold; text-decoration: none;">5</del> z<del style="font-weight: bold; text-decoration: none;">-8</del> a^<del style="font-weight: bold; text-decoration: none;">3</del> <del style="font-weight: bold; text-decoration: none;">z</del>-<del style="font-weight: bold; text-decoration: none;">12</del> a z<del style="font-weight: bold; text-decoration: none;">-</del>7 z a^{-1} -<del style="font-weight: bold; text-decoration: none;">2</del> z a^{-<del style="font-weight: bold; text-decoration: none;">3</del>} <del style="font-weight: bold; text-decoration: none;">-a^6</del>+<del style="font-weight: bold; text-decoration: none;">3</del> a^<del style="font-weight: bold; text-decoration: none;">4</del>+<del style="font-weight: bold; text-decoration: none;">11</del> <del style="font-weight: bold; text-decoration: none;">a</del>^<del style="font-weight: bold; text-decoration: none;">2+</del>3 a^{-<del style="font-weight: bold; text-decoration: none;">2</del>} <del style="font-weight: bold; text-decoration: none;">+11+2</del> a<del style="font-weight: bold; text-decoration: none;">^3</del> z^{-1} +2 a z^{-1} <del style="font-weight: bold; text-decoration: none;">-a^4 </del>z^{<del style="font-weight: bold; text-decoration: none;">-2</del>} -<del style="font-weight: bold; text-decoration: none;">2</del> <del style="font-weight: bold; text-decoration: none;">a</del>^<del style="font-weight: bold; text-decoration: none;">2</del> z^<del style="font-weight: bold; text-decoration: none;">{</del>-<del style="font-weight: bold; text-decoration: none;">2}</del> - z^{-2} &lt;/math&gt;</div></td> <td class="diff-marker" data-marker="+"></td> <td style="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;"><div>&lt;math&gt;a^<ins style="font-weight: bold; text-decoration: none;">6</ins> z^<ins style="font-weight: bold; text-decoration: none;">6-</ins>3 a^<ins style="font-weight: bold; text-decoration: none;">6</ins> z^<ins style="font-weight: bold; text-decoration: none;">4</ins>+<ins style="font-weight: bold; text-decoration: none;">3</ins> a^<ins style="font-weight: bold; text-decoration: none;">6</ins> z^<ins style="font-weight: bold; text-decoration: none;">2-</ins>a^<ins style="font-weight: bold; text-decoration: none;">6</ins>+<ins style="font-weight: bold; text-decoration: none;">3</ins> a^<ins style="font-weight: bold; text-decoration: none;">5</ins> z^<ins style="font-weight: bold; text-decoration: none;">7-</ins>8 a^<ins style="font-weight: bold; text-decoration: none;">5</ins> z^<ins style="font-weight: bold; text-decoration: none;">5</ins>+z^<ins style="font-weight: bold; text-decoration: none;">5</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">5</ins>} +<ins style="font-weight: bold; text-decoration: none;">5</ins> a^5 z^3-<ins style="font-weight: bold; text-decoration: none;">2</ins> z^<ins style="font-weight: bold; text-decoration: none;">3</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">5</ins>} -a^<ins style="font-weight: bold; text-decoration: none;">5</ins> z<ins style="font-weight: bold; text-decoration: none;">+4</ins> a^4 z^<ins style="font-weight: bold; text-decoration: none;">8</ins>-<ins style="font-weight: bold; text-decoration: none;">8</ins> a^<ins style="font-weight: bold; text-decoration: none;">4</ins> z^6<ins style="font-weight: bold; text-decoration: none;">+3</ins> z^6 a^{-<ins style="font-weight: bold; text-decoration: none;">4</ins>} +<ins style="font-weight: bold; text-decoration: none;">a^4</ins> z^<ins style="font-weight: bold; text-decoration: none;">4-</ins>6<ins style="font-weight: bold; text-decoration: none;"> z^4</ins> a^{-4} -<ins style="font-weight: bold; text-decoration: none;">2 a^4</ins> z^<ins style="font-weight: bold; text-decoration: none;">2+z^2 a^{</ins>-<ins style="font-weight: bold; text-decoration: none;">4}</ins> <ins style="font-weight: bold; text-decoration: none;">-</ins>a^<ins style="font-weight: bold; text-decoration: none;">4</ins> z^<ins style="font-weight: bold; text-decoration: none;">{</ins>-<ins style="font-weight: bold; text-decoration: none;">2}</ins> <ins style="font-weight: bold; text-decoration: none;">+</ins>3 <ins style="font-weight: bold; text-decoration: none;">a</ins>^<ins style="font-weight: bold; text-decoration: none;">4</ins>+3 a<ins style="font-weight: bold; text-decoration: none;">^3</ins> z^<ins style="font-weight: bold; text-decoration: none;">9</ins>-<ins style="font-weight: bold; text-decoration: none;">a^3</ins> z^<ins style="font-weight: bold; text-decoration: none;">7+</ins>5<ins style="font-weight: bold; text-decoration: none;"> z^7</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">3</ins>} -<ins style="font-weight: bold; text-decoration: none;">13</ins> <ins style="font-weight: bold; text-decoration: none;">a</ins>^<ins style="font-weight: bold; text-decoration: none;">3</ins> <ins style="font-weight: bold; text-decoration: none;">z</ins>^<ins style="font-weight: bold; text-decoration: none;">5</ins>-<ins style="font-weight: bold; text-decoration: none;">11</ins> z^5 a^{-<ins style="font-weight: bold; text-decoration: none;">3</ins>} +<ins style="font-weight: bold; text-decoration: none;">14</ins> a^<ins style="font-weight: bold; text-decoration: none;">3</ins> z^<ins style="font-weight: bold; text-decoration: none;">3</ins>+<ins style="font-weight: bold; text-decoration: none;">7</ins> z^<ins style="font-weight: bold; text-decoration: none;">3</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">3</ins>} -<ins style="font-weight: bold; text-decoration: none;">8</ins> <ins style="font-weight: bold; text-decoration: none;">a</ins>^<ins style="font-weight: bold; text-decoration: none;">3 z-2 z</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">3</ins>} +<ins style="font-weight: bold; text-decoration: none;">2</ins> a^<ins style="font-weight: bold; text-decoration: none;">3</ins> z^<ins style="font-weight: bold; text-decoration: none;">{-1}</ins> <ins style="font-weight: bold; text-decoration: none;">+</ins>a^<ins style="font-weight: bold; text-decoration: none;">2</ins> z^<ins style="font-weight: bold; text-decoration: none;">{10}</ins>+<ins style="font-weight: bold; text-decoration: none;">8</ins> a<ins style="font-weight: bold; text-decoration: none;">^2</ins> z^<ins style="font-weight: bold; text-decoration: none;">8</ins>+<ins style="font-weight: bold; text-decoration: none;">6</ins> z^<ins style="font-weight: bold; text-decoration: none;">8</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">2</ins>} <ins style="font-weight: bold; text-decoration: none;">-30</ins> <ins style="font-weight: bold; text-decoration: none;">a</ins>^<ins style="font-weight: bold; text-decoration: none;">2</ins> <ins style="font-weight: bold; text-decoration: none;">z</ins>^<ins style="font-weight: bold; text-decoration: none;">6</ins>-<ins style="font-weight: bold; text-decoration: none;">16</ins> z^<ins style="font-weight: bold; text-decoration: none;">6</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">2</ins>} +<ins style="font-weight: bold; text-decoration: none;">39</ins> a^<ins style="font-weight: bold; text-decoration: none;">2</ins> z^<ins style="font-weight: bold; text-decoration: none;">4+21</ins> <ins style="font-weight: bold; text-decoration: none;">z</ins>^4 <ins style="font-weight: bold; text-decoration: none;">a</ins>^<ins style="font-weight: bold; text-decoration: none;">{-</ins>2<ins style="font-weight: bold; text-decoration: none;">} </ins>-28 a^2 z^2-13 z^2 a^{-2} <ins style="font-weight: bold; text-decoration: none;">-</ins>2 a<ins style="font-weight: bold; text-decoration: none;">^2 z</ins>^{-<ins style="font-weight: bold; text-decoration: none;">2</ins>} <ins style="font-weight: bold; text-decoration: none;">+11</ins> <ins style="font-weight: bold; text-decoration: none;">a</ins>^2<ins style="font-weight: bold; text-decoration: none;">+3 a^{</ins>-<ins style="font-weight: bold; text-decoration: none;">2} +7 </ins>a<ins style="font-weight: bold; text-decoration: none;"> z</ins>^<ins style="font-weight: bold; text-decoration: none;">9+4</ins> z<ins style="font-weight: bold; text-decoration: none;">^9</ins> a^<ins style="font-weight: bold; text-decoration: none;">{-1}</ins> -<ins style="font-weight: bold; text-decoration: none;">14</ins> a z<ins style="font-weight: bold; text-decoration: none;">^</ins>7<ins style="font-weight: bold; text-decoration: none;">-5</ins> z<ins style="font-weight: bold; text-decoration: none;">^7</ins> a^{-1} <ins style="font-weight: bold; text-decoration: none;">+3 a z^5</ins>-<ins style="font-weight: bold; text-decoration: none;">4</ins> z<ins style="font-weight: bold; text-decoration: none;">^5</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">1</ins>} +<ins style="font-weight: bold; text-decoration: none;">16</ins> a<ins style="font-weight: bold; text-decoration: none;"> z</ins>^<ins style="font-weight: bold; text-decoration: none;">3</ins>+<ins style="font-weight: bold; text-decoration: none;">16</ins> <ins style="font-weight: bold; text-decoration: none;">z</ins>^3 a^{-<ins style="font-weight: bold; text-decoration: none;">1</ins>} <ins style="font-weight: bold; text-decoration: none;">-12</ins> a z<ins style="font-weight: bold; text-decoration: none;">-7 z a</ins>^{-1} +2 a z^{-1} <ins style="font-weight: bold; text-decoration: none;">+</ins>z^{<ins style="font-weight: bold; text-decoration: none;">10</ins>}<ins style="font-weight: bold; text-decoration: none;">+10</ins> <ins style="font-weight: bold; text-decoration: none;">z^8</ins>-<ins style="font-weight: bold; text-decoration: none;">40</ins> <ins style="font-weight: bold; text-decoration: none;">z</ins>^<ins style="font-weight: bold; text-decoration: none;">6+62</ins> z^<ins style="font-weight: bold; text-decoration: none;">4</ins>-<ins style="font-weight: bold; text-decoration: none;">37</ins> <ins style="font-weight: bold; text-decoration: none;">z^2</ins>- z^{-2} <ins style="font-weight: bold; text-decoration: none;">+11</ins>&lt;/math&gt;</div></td> </tr> </table>

ScottDataRobot https://katlas.org/index.php?title=Data:L11a449/Kauffman_Polynomial&diff=79178&oldid=prev 2005-08-26T18:37:19Z

<p></p> <p><b>New page</b></p><div>&lt;math&gt;a^2 z^{10}+z^{10}+3 a^3 z^9+7 a z^9+4 z^9 a^{-1} +4 a^4 z^8+8 a^2 z^8+6 z^8 a^{-2} +10 z^8+3 a^5 z^7-a^3 z^7-14 a z^7-5 z^7 a^{-1} +5 z^7 a^{-3} +a^6 z^6-8 a^4 z^6-30 a^2 z^6-16 z^6 a^{-2} +3 z^6 a^{-4} -40 z^6-8 a^5 z^5-13 a^3 z^5+3 a z^5-4 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} -3 a^6 z^4+a^4 z^4+39 a^2 z^4+21 z^4 a^{-2} -6 z^4 a^{-4} +62 z^4+5 a^5 z^3+14 a^3 z^3+16 a z^3+16 z^3 a^{-1} +7 z^3 a^{-3} -2 z^3 a^{-5} +3 a^6 z^2-2 a^4 z^2-28 a^2 z^2-13 z^2 a^{-2} +z^2 a^{-4} -37 z^2-a^5 z-8 a^3 z-12 a z-7 z a^{-1} -2 z a^{-3} -a^6+3 a^4+11 a^2+3 a^{-2} +11+2 a^3 z^{-1} +2 a z^{-1} -a^4 z^{-2} -2 a^2 z^{-2} - z^{-2} &lt;/math&gt;</div>

ScottDataRobot