Combinatorial description of plethysm coefficients

Develop a combinatorial description of plethysm coefficients, namely the coefficients of Schur functions in plethysms of Schur functions.

Background

Plethysm coefficients encode multiplicities of irreducible general linear group representations in plethysms of Schur functors. Although they are known to be nonnegative from representation theory, their general combinatorial structure is poorly understood. The paper notes that Stanley posed the problem of finding a combinatorial description, while indicating that the problem appears to be beyond current methods.