Moscow Mathematical Journal

Volume 18, Issue 4, October–December 2018 pp. 667–679.

Gorenstein Properties and Integer Decomposition Properties of Lecture Hall Polytopes

Authors: Takayuki Hibi (1), McCabe Olsen (2) and Akiyoshi Tsuchiya (1)
Author institution:(1) Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
(2) Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA

Summary:

Though much is known about s-lecture hall polytopes, there are still many unanswered questions. In this paper, we show that slecture hall polytopes satisfy the integer decomposition property (IDP) in the case of monotonic s-sequences. Given restrictions on a monotonic s-sequence, we discuss necessary and sufficient conditions for the Fano, reflexive and Gorenstein properties. Additionally, we give a construction for producing Gorenstein/IDP lecture hall polytopes.

2010 Math. Subj. Class. 05A20, 05E40, 13P20, 52B20.

Keywords: Lecture hall polytopes, Gorenstein polytopes, integer decomposition property.

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