Séminaire Lotharingien de Combinatoire, 95B.46 (2026), 12 pp.

Daniel Hwang, Juliet Whidden and Josephine Yu

Computing Parametric Weighted Ehrhart Polynomials of Smooth Polytopes

Abstract. We show that when integral polytopes are deformed while keeping the same facet normal vectors, the coefficients of weighted Ehrhart and h^{*-polynomials are piecewise polynomial
functions in the "right hand sides" of the linear inequalities
defining the polytopes. We give an algorithm and an implementation in
SageMath for computing these polynomials for smooth polytopes, such as
type A alcoved polytopes, using a weighted Euler-Maclaurin type
formula by Khovanskiǐ and Pukhlikov. We discuss some natural
questions concerning signs of the coefficients of the weighted
h^*-polynomials.

Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.

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