Quasisymmetric expansion of Hall-Littlewood symmetric functions

In our previous works we introduced a q-deformation of the generating functions for enriched P-partitions. We call the evaluation of this generating functions on labelled chains, the q-fundamental quasisymmetric functions. These functions interpolate between Gessel's fundamental ($q=0$) and Stembridge's peak ($q=1$) functions, the natural quasisymmetric expansions of Schur and Schur's Q-symmetric functions. In this paper, we show that our q-fundamental functions provide a quasisymmetric expansion of Hall-Littlewood S-symmetric functions with parameter $t=-q$.