Quasisymmetric expansions of Schur-function plethysms

Loehr, Nicholas; Warrington, Gregory

doi:10.1090/S0002-9939-2011-10999-7

Quasisymmetric expansions of Schur-function plethysms
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by Nicholas A. Loehr and Gregory S. Warrington PDF

Proc. Amer. Math. Soc. 140 (2012), 1159-1171 Request permission

Abstract:

Let $s_{\mu }$ denote a Schur symmetric function and $Q_{\alpha }$ a fundamental quasisymmetric function. Explicit combinatorial formulas are developed for the fundamental quasisymmetric expansions of the plethysms $s_{\mu }[s_{\nu }]$ and $s_{\mu }[Q_{\alpha }]$, 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.

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