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INVITED PAPER ON PRODUCTS OF CONJUGACY CLASSES OF THE SYMMETRIC GROUP

Alain Goupil

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Abstract

The product of conjugacy classes of the symmetric group 6, in its group algebra is found as a linear combination of conjugacy classes with integer coefficients. The purpose of this paper is to give a partial answer to the problem of finding simple combinatorial rules to obtain these coefficients. In particular, we will show that the product C@)* C”” of the class of circular permutations with itself can be decomposed in a simple manner.

About this research paper

What this paper is about

The product of conjugacy classes of the symmetric group 6, in its group algebra is found as a linear combination of conjugacy classes with integer coefficients. The purpose of this paper is to give a partial answer to the problem of finding simple combinatorial rules to obtain these coefficients. In particular, we will show that the product C@)* C”” of the class of circular permutations with itself can be decomposed in a simple manner.

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Available abstract

The product of conjugacy classes of the symmetric group 6, in its group algebra is found as a linear combination of conjugacy classes with integer coefficients. The purpose of this paper is to give a partial answer to the problem of finding simple combinatorial rules to obtain these coefficients. In particular, we will show that the product C@)* C”” of the class of circular permutations with itself can be decomposed in a simple manner.

Key concepts: Conjugacy class, Mathematics, Symmetric group, Simple (philosophy), Combinatorics, Product (mathematics), Group (periodic table), Integer (computer science)

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