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.Comment: 14 pages. To appear in Annals of Combinatoric

Liu, Fu

Stanley, Richard P.

Annals of Combinatorics

English

arXiv

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

eScholarship - University of California

The Lecture Hall Parallelepiped

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.National Science Foundation (U.S.) (Grant DMS-1068625

The Lecture Hall Parallelepiped

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