Nicolas Loehr ; Luis Serrano ; Gregory Warrington - 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) - https://doi.org/10.46298/dmtcs.12813
Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomialsConference paper

Authors: Nicolas Loehr 1,2; Luis Serrano ORCID3; Gregory Warrington 4

  • 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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: symmetric functions,quasisymmetric functions,Hall-Littlewood polynomials,standardization,Young tableaux,noncommutative symmetric functions,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Combinatorial polynomials arising from representations; Funder: National Science Foundation; Code: 1201312

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