LABELLING

Abstract

. Let X be a character table of the symmetric group S n . It is shown that unless n = 4 or n = 6, there is a unique way to assign partitions of n to the rows and columns of X so that for all λ and ν , X λν is equal to χ λ ( ν ), the value of the irreducible character of S n labelled by λ on elements of cycle type ν . Analogous results are proved for alternating groups, and for the Brauer character tables of symmetric and alternating groups.