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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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Additional Information
  • Nicholas A. Loehr
  • Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
  • Email: nloehr@vt.edu
  • Gregory S. Warrington
  • Affiliation: Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401
  • MR Author ID: 677560
  • Email: gwarring@cems.uvm.edu
  • Received by editor(s): May 25, 2010
  • Received by editor(s) in revised form: December 24, 2010
  • Published electronically: July 28, 2011
  • Additional Notes: The first author was supported in part by National Security Agency grant H98230-08-1-0045
    The second author was supported in part by National Security Agency grant H98230-09-1-0023
  • Communicated by: Jim Haglund
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1159-1171
  • MSC (2010): Primary 05E05, 05E10
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10999-7
  • MathSciNet review: 2869102