Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials
Combinatorics
2013-06-20 v3
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.
Keywords
Cite
@article{arxiv.1202.3411,
title = {Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials},
author = {Nicholas A. Loehr and Luis G. Serrano and Gregory S. Warrington},
journal= {arXiv preprint arXiv:1202.3411},
year = {2013}
}
Comments
28 pages; added brief discussion of the Hall-Littlewood Q', typos corrected, added references in response to referee suggestions