Unimodality of h*-polynomials for IDP lattice polytopes

Determine whether the h*-polynomial of every lattice polytope possessing the integer decomposition property is unimodal.

Background

The paper situates this question within Ehrhart theory, where the h*-polynomial encodes the lattice-point enumerator of a lattice polytope. The integer decomposition property requires every lattice point in every positive dilation of the polytope to decompose as a sum of lattice points from the original polytope. The open problem asks whether this algebraic property forces the coefficient sequence of the h*-polynomial to be unimodal.

The paper notes that the question was proposed by Schepers and Van Langenhoven and records partial results, including validity in dimensions at most four. The authors study the question for lattice simplices and prove it when the normalized volume is prime, but the general question for all IDP lattice polytopes remains the explicitly stated unresolved problem.