Séminaire Lotharingien de Combinatoire, 95B.49 (2026), 12 pp.

Elisabeth Bullock and Yuhan Jiang

The Ehrhart Series of Alcoved Polytopes

Abstract. Alcoved polytopes are convex polytopes which are the closure of a union of alcoves in an affine Coxeter arrangement. They are rational polytopes, and therefore have Ehrhart quasipolynomials. We describe a method for computing the generating function of the Ehrhart quasipolynomial, or Ehrhart series, of any alcoved polytope via a particular shelling order of its alcoves. We also show a connection between Early's decorated ordered set partitions and this shelling order for the hypersimplex Δ_2,n.

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

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