Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials

Details Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials

2012-02-15

arxiv.org/abs/1202.3411v1

Mathematics

Combinatorics

20 pages

Scientific paper

We introduce explicit combinatorial interpretations for the coefficients in some of the transition matrices between skew Hall-Littlewood polynomials P_lambda/mu(t), Hivert's quasisymmetric Hall-Littlewood polynomials G_gamma(t), and Gessel's fundamental and monomial quasisymmetric functions, F_alpha and M_beta. More specifically, we provide the following: (1) An expansion of the P_lambda in terms of the G_gamma, (2) expansions of the F_alpha and the M_beta in terms of the G_gamma and (3) 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 starred tableaux.

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