Combinatorial interpretations for Kronecker and plethysm coefficients

Determine combinatorial interpretations for the Kronecker coefficients and plethysm coefficients, thereby identifying natural families of positive combinatorial objects counted by these representation-theoretic multiplicities.

Background

Kronecker and plethysm coefficients are nonnegative integers arising as multiplicities in tensor products and composed representations. Unlike Kostka and Littlewood–Richardson coefficients, which count tableaux in established combinatorial models, no comparably satisfactory combinatorial interpretations are known for Kronecker and plethysm coefficients. The paper frames this as both a central problem in algebraic combinatorics and a question connected to computational complexity, since a suitable positive counting interpretation would typically place the coefficients in #P.