Encyclopedia > Even permutation

  Article Content

Even permutation

An even permutation is a permutation which can be produced by an even number of exchanges (called transpositions). For example, (1 3 2)=(1 2)(1 3) is an even permutation. See symmetric group for an elaboration.

An identity permutation is an even permutation as (1)=(1 2)(1 2).

The composition of two even permutations is again an even permutation, and so is the inverse of an even permutation: the even permutations of n letters form a group, the alternating group on n letters, denoted by An. This is a subgroup of the symmetric group Sn and contains n!/2 permutations.

An odd permutation is a permutation which is not an even permutation, equivalently, it is a product by odd number of transpositions.

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
Digital Rights Management

... management, commonly abbreviated DRM, is an umbrella term for any of several arrangements by which the usage of copyrighted data by someone who has purchased a ...

This page was created in 37.5 ms