WikiJournal of Science/Affine symmetric group/XML

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    <full_title>WikiJournal of Science/Affine symmetric group</full_title>
    <issn media_type='electronic'>2002-4436 / 2470-6345 / 2639-5347</issn>
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     <title>Affine symmetric group</title>
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This is an open access article distributed under the&nbsp;[ Creative Commons Attribution License], which permits unrestricted use, distribution, and reproduction, provided the original author and source are credited.</license-p>
The affine symmetric group is a mathematical structure that describes the symmetries of the number line and the regular triangular tesselation of the plane, as well as related higher dimensional objects.  It is an infinite extension of the symmetric group, which consists of all permutations (rearrangements) of a finite set.  In addition to its geometric description, the affine symmetric group may be defined as the collection of permutations of the integers (..., &minus;2, &minus;1, 0, 1, 2, ...) that are periodic in a certain sense, or in purely algebraic terms as a group with certain generators and relations.  These different definitions allow for the extension of many important properties of the finite symmetric group to the infinite setting, and are studied as part of the fields of combinatorics and representation theory.