Unimodality for IDP Lattice Simplices of Prime Normalized Volume
Feihu Liu, Zihao Zhang
Source abstract
Recently, Ferroni constructed a family of counterexamples to the well-known conjecture in Ehrhart theory stating that the -polynomial of a lattice polytope with the integer decomposition property is unimodal. This raises the question of whether the -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 -polynomial. Furthermore, we establish several sufficient conditions for the unimodality of the -polynomial of such simplices.
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