Quasisymmetric expansions of Schur-function plethysms

Loehr, Nicholas; Warrington, Gregory

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

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ISSN 1088-6826(online) ISSN 0002-9939(print)

Quasisymmetric expansions of Schur-function plethysms

Authors: Nicholas A. Loehr and Gregory S. Warrington
Journal: Proc. Amer. Math. Soc. 140 (2012), 1159-1171
MSC (2010): Primary 05E05, 05E10
Posted: July 28, 2011
MathSciNet review: 2869102
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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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