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The Lecture Hall Parallelepiped

Author(s)
Liu, Fu; Stanley, Richard P.
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Abstract
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.
Date issued
2014-07
URI
http://hdl.handle.net/1721.1/93191
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Annals of Combinatorics
Publisher
Springer-Verlag
Citation
Liu, Fu, and Richard P. Stanley. “The Lecture Hall Parallelepiped.” Ann. Comb. 18, no. 3 (July 2, 2014): 473–488.
Version: Original manuscript
ISSN
0218-0006
0219-3094

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