2024/02/17 by Jesús A. De Loera, De Loera, Jesús A., Laura Escobar +5 · 3 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2402.11328
openalex publication_date 2024/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.