Unimodality for IDP Lattice Simplices of Prime Normalized Volume

Abstract: Recently, Ferroni constructed a family of counterexamples to the well-known conjecture in Ehrhart theory stating that the $h<sup>*$-polynomial of a lattice polytope with the integer decomposition property is unimodal. This raises the question of whether the $h<sup>*$-polynomial of a lattice simplex with the integer decomposition property remains unimodal. In this note, we prove that every lattice simplex with the integer decomposition property and prime normalized volume has a unimodal $h<sup>*$-polynomial. Furthermore, we establish several sufficient conditions for the unimodality of the $h<sup>*$-polynomial of such simplices.