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The Poset of Conjugacy Classes and Decomposition of Products in the Symmetric Group

Published online by Cambridge University Press:  20 November 2018

François Bédard  and
Alain Goupil
François Bédard
Affiliation:
Département de mathématiques et d'informatique, Université du Québec à Montréal, C.P. 8888 succ.A, Montréal, Québec H3C 3P8
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Abstract

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The action by multiplication of the class of transpositions of the symmetric group on the other conjugacy classes defines a graded poset as described by Birkhoff ([2]). In this paper, the edges of this poset are given a weight and the structure obtained is called the poset of conjugacy classes of the symmetric group. We use weights of chains in the posets to obtain new formulas for the decomposition of products of conjugacy classes of the symmetric group in its group algebra as linear combinations of conjugacy classes and we derive a new identity involving partitions of n.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 2 , 01 June 1992 , pp. 152 - 160
Copyright
Copyright © Canadian Mathematical Society 1992 

Footnotes

1

Partially supported by the FCAR (Québec)

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