Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope

2007/03/01 by Velleda Baldoni, Baldoni, Velleda, Nicole Berline +3
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/0703031

openalex publication_date 2007/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend to Barvinok's valuations the Euler-Maclaurin expansion formula which we obtained previously for the sum of values of a polynomial over the integral points of a rational polytope. This leads to an improvement of Barvinok's polynomial type algorithm for computing the highest coefficients of the corresponding Ehrhart quasi-polynomial.

Related

• Highest coefficients of weighted Ehrhart quasi-polynomials for a rational polytope
• Local Euler-Maclaurin formula for polytopes
• Rational Ehrhart quasi-polynomials
• Sum-integral interpolators and the Euler-Maclaurin formula for polytopes
• Computing the Ehrhart quasi-polynomial of a rational simplex