## Quasisymmetric expansions of Schur-function plethysms

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- by Nicholas A. Loehr and Gregory S. Warrington PDF
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**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.## References

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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