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<?xml version="1.0" encoding="UTF-8" ?>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 >script type="text/javascript" "https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML " >script >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_mj.html" >Top</a> <a href="chap1_mj.html" >1</a> <a href="chap2_mj.html" >2</a> <a href="chap3_mj.html" >3</a> <a href="chap4_mj.html" >4</a> <a href="chap5_mj.html" >5</a> <a 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href="chap7_mj.html#X820405DB787A5D32" >7.1-1 PermComplement</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X8453836D83A63E54" >7.2 <span class="Heading" > Rank Encoding </span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7F1000E882050AFF" >7.2-1 IsRankEncoding</a></span >div ></div >div >span class="Heading" >Some Permutation Essentials</span ></h3>h.</p>"X80E3E5BB8156C6A1" name="X80E3E5BB8156C6A1" ></a></p>span class="Heading" > Complement </span ></h4>"X820405DB787A5D32" name="X820405DB787A5D32" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ PermComplement</code >( <var class="Arg" >perm</var > )</td ><td class="tdright" >( function )</td ></tr ></table ></div >code class="code" >perm</code >.</p>span class="SimpleMath" >\(\tau=\tau_{1}\ldots\tau_{n}\)</span > is the permutation</p>"center" >\[\tau^{C}=(n+1)-\tau_{1}\ \ (n+1)-\tau_{2}\ldots (n+1)-\tau_{n}\]</p>div class="example" ><pre >span class="GAPprompt" >gap></span > <span class="GAPinput" >PermComplement([3,2,8,6,7,1,5,4]);</span >span class="GAPprompt" >gap></span > <span class="GAPinput" ></span ></pre ></div >"X8453836D83A63E54" name="X8453836D83A63E54" ></a></p>span class="Heading" > Rank Encoding </span ></h4>"X7F1000E882050AFF" name="X7F1000E882050AFF" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsRankEncoding</code >( <var class="Arg" >perm</var > )</td ><td class="tdright" >( function )</td ></tr ></table ></div >code class="code" >true</code > if <code class="code" >perm</code > is a valid rank encoding of a permutation.</p>code class="code" >IsRankEncoding</code > checkes whether the input list <code class="code" >perm</code > is a valid rank encoding by checking whether it is accepted by the bounded class automaton, with the highest rank being set by the highest element in <code class="code" >perm</code >.</p>div class="example" ><pre >span class="GAPprompt" >gap></span > <span class="GAPinput" >IsRankEncoding([3,2,6,4,4,1,2,1]);</span >span class="GAPprompt" >gap></span > <span class="GAPinput" >IsRankEncoding([3,2,6,4,5,1,2,1]);</span >span class="GAPprompt" >gap></span > <span class="GAPinput" ></span ></pre ></div >div class="chlinkprevnextbot" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap6_mj.html" >[Previous Chapter]</a> <a href="chap8_mj.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0_mj.html" >Top</a> <a href="chap1_mj.html" >1</a> <a href="chap2_mj.html" >2</a> <a href="chap3_mj.html" >3</a> <a href="chap4_mj.html" >4</a> <a href="chap5_mj.html" >5</a> <a href="chap6_mj.html" >6</a> <a href="chap7_mj.html" >7</a> <a href="chap8_mj.html" >8</a> <a 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