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arXiv · 1202.3411

Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials

Nicholas A. Loehr·Luis G. Serrano·Gregory S. Warrington
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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: 1) the G-expansions of the Hall-Littlewood polynomials P_lambda, the monomial quasisymmetric polynomials M_alpha, the quasisymmetric Schur polynomials S_alpha, and the peak quasisymmetric functions K_alpha; 2) an expansion of P_lambda/mu in terms of the F_alpha's. The F-expansion of P_lambda/mu is facilitated by introducing starred tableaux.

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Nicholas A. Loehr, Luis G. Serrano, Gregory S. Warrington. 2012-02-15. Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials. https://arxiv.org/abs/1202.3411

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