Some computations regarding Foulkes' conjecture

Abstract

We describe how certain permutation actions of large symmetric groups can be efficiently implemented on a computer. Using a specially tailored adaptation of a general technique to enumerate huge orbits and substantial distributed computation on a cluster of workstations, we collect further evidence related to the approach to Foulkes' conjecture suggested in “A Note on Plethysm,” by S. C. Black and R. J. List.