Symmetric Function Algebra on a Computer

AbstractAlgorithms and codes are developed for problems related to the theory of symmetric functions. Their uses are illustrated by application to the calculation of transition matrices between different symmetric function bases, multiplication and linear combination of symmetric functions, and the calculation of group characters. On a modern computer, the algorithms require less than a minute to find all the irreducible characters of the symmetric group of order 20, to express all Schur functions of weights up to 20 in terms of monomial symmetric functions, or to compute the multiplication table for all Schur functions of weights up 10, with products expressed as linear combinations of Schur functions