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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.06511 |
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| _version_ | 1866912041875275776 |
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| author | Reiner, Victor Rhoades, Brendon |
| author_facet | Reiner, Victor Rhoades, Brendon |
| contents | The Ehrhart polynomial and Ehrhart series count lattice points in integer dilations of a lattice polytope. We introduce and study a $q$-deformation of the Ehrhart series, based on the notions of harmonic spaces and Macaulay's inverse systems for coordinate rings of finite point configurations. We conjecture that this $q$-Ehrhart series is a rational function, and introduce and study a bigraded algebra whose Hilbert series matches the $q$-Ehrhart series. Defining this algebra requires a new result on Macaulay inverse systems for Minkowski sums of point configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Harmonics and graded Ehrhart theory Reiner, Victor Rhoades, Brendon Combinatorics Commutative Algebra The Ehrhart polynomial and Ehrhart series count lattice points in integer dilations of a lattice polytope. We introduce and study a $q$-deformation of the Ehrhart series, based on the notions of harmonic spaces and Macaulay's inverse systems for coordinate rings of finite point configurations. We conjecture that this $q$-Ehrhart series is a rational function, and introduce and study a bigraded algebra whose Hilbert series matches the $q$-Ehrhart series. Defining this algebra requires a new result on Macaulay inverse systems for Minkowski sums of point configurations. |
| title | Harmonics and graded Ehrhart theory |
| topic | Combinatorics Commutative Algebra |
| url | https://arxiv.org/abs/2407.06511 |