# Algorithms for the character theory of the symmetric group

## Abstract

Description of a comprehensive package of routines for the character theory of the symmetric groups S_{n} have been presented. The efficiency of these algorithms derives from the reduction of the expansions of plethysms and Kronecker products to multiplication of Schur functions. This in turn is done with minimal computational effort by making use of an algorithmic modification of the LR rule due to Remmel and Whitney.

Existing implementations of a number of these algorithms turned out to be very efficient. The calculation of totally symmetric and antisymmetric plethysms for instance, could be carried out further than the existing tables in the literature.

The package is centered around a core which coordinates the various primitives and sequentially invokes the necessary routines to carry out the required calculations. The common features of the various algorithms implemented make it possible to construct this package in a highly modular and compact form in a UNIX environment.

## Keywords

Irreducible Representation Symmetric Group Symmetric Function Kronecker Product Irreducible Character## Preview

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