Quasisymmetric expansions of Schur-function plethysms

Abstract

Let s μ denote a Schur symmetric function and Q α a fundamental quasisymmetric function. Explicit combinatorial formulas are developed for the fundamental quasisymmetric expansions of the plethysms s μ[s ν] and s μ[Q α], as well as for related plethysms defined by inequality conditions. The key tools for obtaining these expansions are new standardization and reading word constructions for matrices. © 2011 American Mathematical Society.