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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/2402.11328 |
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| _version_ | 1866929246608293888 |
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| author | De Loera, Jesús A. Escobar, Laura Kaplan, Nathan Wang, Chengyang |
| author_facet | De Loera, Jesús A. Escobar, Laura Kaplan, Nathan Wang, Chengyang |
| contents | We study the problem of counting lattice points of a polytope that are weighted by an Ehrhart quasi-polynomial of a family of parametric polytopes. As applications one can compute integrals and maximum values of such quasi-polynomials, as well as obtain new identities in representation theory. These topics have been of great interest to Michèle Vergne since the late 1980's. Our new contribution is a result that transforms weighted sums into unweighted sums, even when the weights are very general quasipolynomials. In some cases it leads to faster integration over a polytope. We can create new algebraic identities and conjectures in algebraic combinatorics and number theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11328 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sums of Weighted Lattice Points of Polytopes De Loera, Jesús A. Escobar, Laura Kaplan, Nathan Wang, Chengyang Combinatorics Number Theory We study the problem of counting lattice points of a polytope that are weighted by an Ehrhart quasi-polynomial of a family of parametric polytopes. As applications one can compute integrals and maximum values of such quasi-polynomials, as well as obtain new identities in representation theory. These topics have been of great interest to Michèle Vergne since the late 1980's. Our new contribution is a result that transforms weighted sums into unweighted sums, even when the weights are very general quasipolynomials. In some cases it leads to faster integration over a polytope. We can create new algebraic identities and conjectures in algebraic combinatorics and number theory. |
| title | Sums of Weighted Lattice Points of Polytopes |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2402.11328 |