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 Pλ/μ(t) and Hivertʼs quasisymmetric Hall–Littlewood polynomials Gγ(t). More specifically, we provide:1.the G-expansions of the Hall–Littlewood polynomials Pλ(t), the monomial quasisymmetric polynomials Mα, the quasisymmetric Schur polynomials Sα, and the peak quasisymmetric functions Kα;2.an expansion of Pλ/μ(t) in terms of the Fαʼs. The F-expansion of Pλ/μ(t) is facilitated by introducing starred tableaux.