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<title>GNU Scientific Library &ndash; Reference Manual: Permutations</title>

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<a name="Permutations"></a>
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<p>
Next: <a href="Combinations.html#Combinations" accesskey="n" rel="next">Combinations</a>, Previous: <a href="Vectors-and-Matrices.html#Vectors-and-Matrices" accesskey="p" rel="previous">Vectors and Matrices</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Permutations-1"></a>
<h2 class="chapter">9 Permutations</h2>
<a name="index-permutations"></a>

<p>This chapter describes functions for creating and manipulating
permutations. A permutation <em>p</em> is represented by an array of
<em>n</em> integers in the range 0 to <em>n-1</em>, where each value
<em>p_i</em> occurs once and only once.  The application of a permutation
<em>p</em> to a vector <em>v</em> yields a new vector <em>v'</em> where
<em>v'_i = v_{p_i}</em>. 
For example, the array <em>(0,1,3,2)</em> represents a permutation
which exchanges the last two elements of a four element vector.
The corresponding identity permutation is <em>(0,1,2,3)</em>.   
</p>
<p>Note that the permutations produced by the linear algebra routines
correspond to the exchange of matrix columns, and so should be considered
as applying to row-vectors in the form <em>v' = v P</em> rather than
column-vectors, when permuting the elements of a vector.
</p>
<p>The functions described in this chapter are defined in the header file
<samp>gsl_permutation.h</samp>.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="The-Permutation-struct.html#The-Permutation-struct" accesskey="1">The Permutation struct</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Permutation-allocation.html#Permutation-allocation" accesskey="2">Permutation allocation</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Accessing-permutation-elements.html#Accessing-permutation-elements" accesskey="3">Accessing permutation elements</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Permutation-properties.html#Permutation-properties" accesskey="4">Permutation properties</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Permutation-functions.html#Permutation-functions" accesskey="5">Permutation functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Applying-Permutations.html#Applying-Permutations" accesskey="6">Applying Permutations</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Reading-and-writing-permutations.html#Reading-and-writing-permutations" accesskey="7">Reading and writing permutations</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Permutations-in-cyclic-form.html#Permutations-in-cyclic-form" accesskey="8">Permutations in cyclic form</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Permutation-Examples.html#Permutation-Examples" accesskey="9">Permutation Examples</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Permutation-References-and-Further-Reading.html#Permutation-References-and-Further-Reading">Permutation References and Further Reading</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
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