  We introduce and study s-lecture hall P-partitions which is a generalization
of s-lecture hall partitions to labeled (weighted) posets. We provide
generating function identities for s-lecture hall P-partitions that generalize
identities obtained by Savage and Schuster for s-lecture hall partitions, and
by Stanley for P-partitions. We also prove that the corresponding
(P,s)-Eulerian polynomials are real-rooted for certain pairs (P,s), and
speculate on unimodality properties of these polynomials.
