Invariance properties for coefficients of symmetric functions

Abstract

We show that several of the main structural constants for symmetric functions (Littlewood-Richardsoncoefficients, Kronecker coefficients, plethysm coefficients, and the Kostka–Foulkes polynomials) share invarianceproperties related to the operations of taking complements with respect to rectangles and adding rectangles.

Keywords

• kostka coefficients
• plethysm coefficients
• kronecker coefficients
• littlewood-richardson coefficients
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]