Transition matrices for symmetric and quasisymmetric Hall–Littlewood polynomials

We introduce explicit combinatorial interpretations for the coefficients in some of the transition matrices relating to skew Hall–Littlewood polynomials P λ / μ ( t ) and Hivertʼs quasisymmetric Hall–Littlewood polynomials G γ ( t ) . More specifically, we provide:1. expansions of the Hall–Littlewood polynomials P λ ( t ) , the monomial quasisymmetric polynomials M α , the quasisymmetric Schur polynomials S α , and the peak quasisymmetric functions K α ; ansion of P λ / μ ( t ) in terms of the F α ʼs. -expansion of P λ / μ ( t ) is facilitated by introducing starred tableaux.