Gorenstein properties and integer decomposition properties of lecture hall polytopes
| Autor: | Akiyoshi Tsuchiya, Takayuki Hibi, McCabe Olsen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Property (philosophy)
General Mathematics 010102 general mathematics Polytope Monotonic function Fano plane Condensed Matter::Mesoscopic Systems and Quantum Hall Effect 01 natural sciences Lecture hall Combinatorics 0103 physical sciences FOS: Mathematics Mathematics::Metric Geometry Mathematics - Combinatorics Combinatorics (math.CO) 010307 mathematical physics 0101 mathematics Integer factorization Mathematics |
| Popis: | Though much is known about ${\bf s}$-lecture hall polytopes, there are still many unanswered questions. In this paper, we show that ${\bf s}$-lecture hall polytopes satisfy the integer decomposition property (IDP) in the case of monotonic ${\bf s}$-sequences. Given restrictions on a monotonic ${\bf s}$-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. 14 pages; Two references added; partially rewritten introduction and concluding remarks sections |
| Databáze: | OpenAIRE |
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