The Lecture Hall Parallelepiped
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Stanley_The lecture.pdf
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175.82 KB
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Author(s)
Liu, Fu
Stanley, Richard P.
Date Issued
July 2014
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00026-014-0235-8
