The Lecture Hall Parallelepiped

Abstract

The s-lecture hall polytopes P s are a class of integer polytopes defined by Savage and Schuster which are closely related to the lecture hall partitions of Eriksson and Bousquet-Melou. We define a half-open parallelopiped Par s associated with P s and give a simple description of its integer points. We use this description to recover earlier results of Savage et al. on the δ-vector (or h*-vector) and to obtain the connections to s-ascents and s-descents, as well as some generalizations of these results.