Towards a combinatorial classification of skew Schur functions

Abstract

We present a single operation for constructing skew diagrams whose corresponding skew Schur functions are equal. This combinatorial operation naturally generalises and unifies all results of this type to date. Moreover, our operation suggests a closely related condition that we conjecture is necessary and sufficient for skew diagrams to yield equal skew Schur functions.Comment: 34 pages, 2 figures. Minor changes. Final version, to appear in Transactions of the AM