The Lecture Hall Parallelepiped
نویسندگان
چکیده
The s-lecture hall polytopes Ps 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 Pars associated with Ps 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.
منابع مشابه
Lecture hall partitions and the wreath products
It is shown that statistics on the wreath product groups, Ck oSn, can be interpreted in terms of natural statistics on lecture hall partitions. Lecture hall theory is applied to prove distribution results for statistics on Ck oSn. Finally, some new statistics on Ck oSn are introduced, inspired by lecture hall theory, and their distributions are derived.
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It is shown that statistics on the wreath product groups, Ck �Sn, can be interpreted in terms of natural statistics on lecture hall partitions. Lecture hall theory is applied to prove distribution results for statistics on Ck � Sn. Finally, some new statistics on Ck � Sn are introduced, inspired by lecture hall theory, and their distributions are derived.
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