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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head> <title>GAP (PatternClass) - Chapter 7: Some Permutation Essentials</title> <meta http-equiv="content-type" content="text/html; charset=UTF-8" /> <meta name="generator" content="GAPDoc2HTML" /> <link rel="stylesheet" type="text/css" href="manual.css" /> <script src="manual.js" type="text/javascript"></script> <script type="text/javascript">overwriteStyle();</script> </head> <body class="chap7" onload="jscontent()"> <div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a <div class="chlinkprevnexttop"> <a href="chap0.html">[Top of Book]</a> <a href="chap0.html#con <p id="mathjaxlink" class="pcenter"><a href="chap7_mj.html">[MathJax on]</a></p> <p><a id="X81DB657E7FEF0295" name="X81DB657E7FEF0295"></a></p> <div class="ChapSects"><a href="chap7.html#X81DB657E7FEF0295">7 <span class="Heading">Some <div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X8 </span> <div class="ContSSBlock"> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X820405DB787A5D32">7 </div></div> <div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X8 </span> <div class="ContSSBlock"> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7F1000E882050AFF">7 </div></div> </div> <h3>7 <span class="Heading">Some Permutation Essentials</span></h3> <p>In this chapter we mention a couple functions that are fairly basic but useful tools to work wit <p><a id="X80E3E5BB8156C6A1" name="X80E3E5BB8156C6A1"></a></p> <h4>7.1 <span class="Heading"> Complement </span></h4> <p><a id="X820405DB787A5D32" name="X820405DB787A5D32"></a></p> <h5>7.1-1 PermComplement</h5> <div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Pe <p>Returns: The permutation that is the complement of <code class="code">perm</code>.</p> <p>The complement of a permutation <span class="SimpleMath">τ=τ_1...τ_n</span> is the permutation</ <p class="pcenter">τ^C=(n+1)-τ_1 (n+1)-τ_2... (n+1)-τ_n</p> <p>.</p> <div class="example"><pre> <span class="GAPprompt">gap></span> <span class="GAPinput">PermComplement([3,2,8,6,7,1,5,4 [ 6, 7, 1, 3, 2, 8, 4, 5 ] <span class="GAPprompt">gap></span> <span class="GAPinput"></span></pre></div> <p><a id="X8453836D83A63E54" name="X8453836D83A63E54"></a></p> <h4>7.2 <span class="Heading"> Rank Encoding </span></h4> <p><a id="X7F1000E882050AFF" name="X7F1000E882050AFF"></a></p> <h5>7.2-1 IsRankEncoding</h5> <div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Is <p>Returns: <code class="code">true</code> if <code class="code">perm</code> is a valid rank encodin <p><code class="code">IsRankEncoding</code> checkes whether the input list <code class="code">pe <div class="example"><pre> <span class="GAPprompt">gap></span> <span class="GAPinput">IsRankEncoding([3,2,6,4,4,1,2,1 true <span class="GAPprompt">gap></span> <span class="GAPinput">IsRankEncoding([3,2,6,4,5,1,2,1 false <span class="GAPprompt">gap></span> <span class="GAPinput"></span></pre></div> <div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a> <a href="chap0.html#con <div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a <hr /> <p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GA </body> </html> ¤ Dauer der Verarbeitung: 0.13 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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