✦ LIBER ✦

A Representation of Even Permutations

✍ Scribed by L. Cangelmi; P. Cellini

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 80 KB
Volume: 19
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1997.0197

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✦ Synopsis

We give a combinatorial proof of the formula giving the number of representations of an even permutation σ in S n as a product of an n-cycle by an (n -2)-cycle, such a number being (nχ(σ ))(n -3)!, where χ(σ ) is the number of fixed points of σ . This proof relies on the fact that any odd permutation in S n is the product of an n-cycle by an (n -1)-cycle in exactly 2(n -2)! different ways.

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