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Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials
Abstract : 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.
https://hal.inria.fr/hal-01229729
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:20:41 AM
Last modification on : Friday, April 16, 2021 - 3:34:01 PM
Long-term archiving on: : Friday, April 28, 2017 - 3:07:46 PM
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:20:41 AM
Last modification on : Friday, April 16, 2021 - 3:34:01 PM
Long-term archiving on: : Friday, April 28, 2017 - 3:07:46 PM
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dmAS0126.pdf
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