Nicolas Loehr ; Luis Serrano ; Gregory Warrington
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Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials
dmtcs:12813 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2013,
DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
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https://doi.org/10.46298/dmtcs.12813
Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomialsConference paper
Authors: Nicolas Loehr 1,2; Luis Serrano 3; Gregory Warrington 4
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Nicolas Loehr;Luis Serrano;Gregory Warrington
1 Department of Mathematics [Blacksburg]
2 Mathematics Department [UNSA Annapolis]
3 Laboratoire de combinatoire et d'informatique mathématique [Montréal]
4 Department of Mathematics & Statistics [Burlington]
We introduce explicit combinatorial interpretations for the coefficients in some of the transition matrices relating to skew Hall-Littlewood polynomials Pλ/μ(x;t) and Hivert's quasisymmetric Hall-Littlewood polynomials Gγ(x;t). More specifically, we provide the following: 1. Gγ-expansions of the Pλ, the monomial quasisymmetric functions, and Gessel's fundamental quasisymmetric functions Fα, and 2. an expansion of the Pλ/μ in terms of the Fα. The Fα expansion of the Pλ/μ is facilitated by introducing the set of starred tableaux. In the full version of the article we also provide Gγ-expansions of the quasisymmetric Schur functions and the peak quasisymmetric functions of Stembridge.