Regular Unimodular Triangulations of Reflexive IDP 2-Supported Weighted Projective Space Simplices
| Autor: | Derek Hanely, Benjamin Braun |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Annals of Combinatorics. 25:935-960 |
| ISSN: | 0219-3094 0218-0006 |
| Popis: | For each integer partition $$\mathbf {q}$$ with d parts, we denote by $$\Delta _{(1,\mathbf {q})}$$ the lattice simplex obtained as the convex hull in $$\mathbb {R}^d$$ of the standard basis vectors along with the vector $$-\mathbf {q}$$ . For $$\mathbf {q}$$ with two distinct parts such that $$\Delta _{(1,\mathbf {q})}$$ is reflexive and has the integer decomposition property, we establish a characterization of the lattice points contained in $$\Delta _{(1,\mathbf {q})}$$ . We then construct a Grobner basis with a squarefree initial ideal of the toric ideal defined by these simplices. This establishes the existence of a regular unimodular triangulation for reflexive 2-supported $$\Delta _{(1,\mathbf {q})}$$ having the integer decomposition property. As a corollary, we obtain a new proof that these simplices have unimodal Ehrhart $$h^*$$ -vectors. |
| Databáze: | OpenAIRE |
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