<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- --> <!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html --> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" > <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head><title>compositions -- compositions of an integer</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_compress.html">next</a> | <a href="_components_lp__Chain__Complex_rp.html">previous</a> | <a href="_compress.html">forward</a> | <a href="_components_lp__Chain__Complex_rp.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div> </td> </tr> </table> <hr/> <div><h1>compositions -- compositions of an integer</h1> <div class="single"><h2>Synopsis</h2> <ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>compositions(k,n)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>k</tt>, <span>an <a href="___Z__Z.html">integer</a></span>, a nonnegative integer</span></li> <li><span><tt>n</tt>, <span>an <a href="___Z__Z.html">integer</a></span>, also nonnegative</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___List.html">list</a></span>, of all of the ways of writing <tt>n</tt> as a sum of exactly <tt>k</tt> nonnegative integers</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : compositions(2,5) o1 = {{5, 0}, {4, 1}, {3, 2}, {2, 3}, {1, 4}, {0, 5}} o1 : List</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_partitions.html" title="list the partitions of an integer">partitions</a> -- list the partitions of an integer</span></li> <li><span><a href="_combinatorial_spfunctions.html" title="">combinatorial functions</a></span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>compositions</tt> :</h2> <ul><li>compositions(ZZ,ZZ)</li> </ul> </div> </div> </body> </html>