{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19637",
  "author_total": 2,
  "authors": [
    {
      "name": "Feihu Liu"
    },
    {
      "name": "Zihao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dp02200k336az.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19637",
  "fulltext_url": null,
  "id": "dp02200k336az",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19637",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213591523",
  "pdf_url": "https://arxiv.org/pdf/2609.19637",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dp02200k336az.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2609.19637",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19637"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Unimodality for IDP Lattice Simplices of Prime Normalized Volume",
  "title_text": "Unimodality for IDP Lattice Simplices of Prime Normalized Volume",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/dp02200k336az",
  "venue": "arXiv",
  "versions": []
}