Decompositions of Ehrhart $h^*$-polynomials for rational polytopes
| Autor: | Beck, Matthias, Braun, Benjamin, Vindas-Meléndez, Andrés R. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Discrete & Computational Geometry 68, no. 1 (2022), 50-71 |
| Druh dokumentu: | Working Paper |
| Popis: | The Ehrhart quasipolynomial of a rational polytope $P$ encodes the number of integer lattice points in dilates of $P$, and the $h^*$-polynomial of $P$ is the numerator of the accompanying generating function. We provide two decomposition formulas for the $h^*$-polynomial of a rational polytope. The first decomposition generalizes a theorem of Betke and McMullen for lattice polytopes. We use our rational Betke--McMullen formula to provide a novel proof of Stanley's Monotonicity Theorem for the $h^*$-polynomial of a rational polytope. The second decomposition generalizes a result of Stapledon, which we use to provide rational extensions of the Stanley and Hibi inequalities satisfied by the coefficients of the $h^*$-polynomial for lattice polytopes. Lastly, we apply our results to rational polytopes containing the origin whose duals are lattice polytopes. Comment: 17 pages, 2 figures, 2 tables |
| Databáze: | arXiv |
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