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arXiv · 2609.19637

Unimodality for IDP Lattice Simplices of Prime Normalized Volume

Feihu Liu·Zihao Zhang
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Abstract

Recently, Ferroni constructed a family of counterexamples to the well-known conjecture in Ehrhart theory stating that the $h^*$-polynomial of a lattice polytope with the integer decomposition property is unimodal. This raises the question of whether the $h^*$-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 $h^*$-polynomial. Furthermore, we establish several sufficient conditions for the unimodality of the $h^*$-polynomial of such simplices.

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Feihu Liu, Zihao Zhang. 2026-09-17. Unimodality for IDP Lattice Simplices of Prime Normalized Volume. https://arxiv.org/abs/2609.19637

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