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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{liu2026unimodality,
  title = {{Unimodality for IDP Lattice Simplices of Prime Normalized Volume}},
  author = {Feihu Liu and Zihao Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.19637},
  eprint = {2609.19637},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19637},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Unimodality for IDP Lattice Simplices of Prime Normalized Volume
AU  - Feihu Liu
AU  - Zihao Zhang
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19637
UR  - https://arxiv.org/abs/2609.19637
AB  - 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.
ER  -