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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
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
Published electronically: 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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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
Email: gwarring@cems.uvm.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10999-7
PII: S 0002-9939(2011)10999-7
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.