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 polynomialsArticle

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 $P_{\lambda / \mu}(x;t)$ and Hivert's quasisymmetric Hall-Littlewood polynomials $G_{\gamma}(x;t)$. More specifically, we provide the following: 1. $G_{\gamma}$-expansions of the $P_{\lambda}$, the monomial quasisymmetric functions, and Gessel's fundamental quasisymmetric functions $F_{\alpha}$, and 2. an expansion of the $P_{\lambda / \mu}$ in terms of the $F_{\alpha}$. The $F_{\alpha}$ expansion of the $P_{\lambda / \mu}$ is facilitated by introducing the set of $\textit{starred tableaux}$. In the full version of the article we also provide $G_{\gamma}$-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]

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