The Lecture Hall Parallelepiped
Fu Liu, Richard P. Stanley

TL;DR
This paper introduces a half-open parallelepiped associated with s-lecture hall polytopes, providing a new way to describe their integer points and recover known results related to their -vector, s-ascents, and s-descents.
Contribution
It defines a novel parallelepiped linked to s-lecture hall polytopes and offers a simplified description of its integer points, connecting to existing combinatorial properties.
Findings
Recovered earlier results on the -vector of P_s
Connected -vector to s-ascents and s-descents
Generalized previous combinatorial results
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-M\'elou. 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 \delta-vector (or h^*-vector) and to obtain the connections to s-ascents and s-descents, as well as some generalizations of these results.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · graph theory and CDMA systems
