Sums of Weighted Lattice Points of Polytopes

Autor:	De Loera, Jesús A., Escobar, Laura, Kaplan, Nathan, Wang, Chengyang
Rok vydání:	2024
Předmět:	Mathematics - Combinatorics Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	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 Mich\`ele 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. Comment: 24 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.11328 Zobrazit plný text záznamu View this record from Arxiv