The Lecture Hall Parallelepiped
Author(s)Liu, Fu; Stanley, Richard P.
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The s-lecture hall polytopes P [subscript 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-Mélou. We define a half-open parallelopiped Par [subscript s] associated with P [subscript 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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Annals of Combinatorics
Liu, Fu, and Richard P. Stanley. “The Lecture Hall Parallelepiped.” Ann. Comb. 18, no. 3 (July 2, 2014): 473–488.