Level Algebras and $\mathbf {s}$-Lecture Hall Polytopes
| Autor: | Florian Kohl, McCabe Olsen |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics::Combinatorics
Property (philosophy) Generalization Semigroup Applied Mathematics Polytope Characterization (mathematics) Condensed Matter::Mesoscopic Systems and Quantum Hall Effect Physics::Classical Physics Lattice (discrete subgroup) Lecture hall Theoretical Computer Science Combinatorics Computational Theory and Mathematics Classification result Physics::Space Physics Mathematics::Metric Geometry Discrete Mathematics and Combinatorics Geometry and Topology Mathematics |
| Zdroj: | The Electronic Journal of Combinatorics. 27 |
| ISSN: | 1077-8926 |
| DOI: | 10.37236/8626 |
| Popis: | Given a family of lattice polytopes, a common endeavor in Ehrhart theory is the classification of those polytopes in the family that are Gorenstein, or more generally level. In this article, we consider these questions for ${\boldsymbol s}$-lecture hall polytopes, which are a family of simplices arising from $\mathbf {s}$-lecture hall partitions. In particular, we provide concrete classifications for both of these properties purely in terms of ${\boldsymbol s}$-inversion sequences. Moreover, for a large subfamily of ${\boldsymbol s}$-lecture hall polytopes, we provide a more geometric classification of the Gorenstein property in terms of its tangent cones. We then show how one can use the classification of level ${\boldsymbol s}$-lecture hall polytopes to construct infinite families of level ${\boldsymbol s}$-lecture hall polytopes, and to describe level ${\boldsymbol s}$-lecture hall polytopes in small dimensions. |
| Databáze: | OpenAIRE |
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