{
  "abstract": "We prove that the Ehrhart $h^*$-polynomials of crown order polytopes are real-rooted, settling a conjecture of Lundström and Saud Maia Leite. For each integer $r\\ge3$, the crown order polytope on $2r$ elements and the rank-$r$ whirl base polytope have the same $h^*$-polynomial. The $h^*$-polynomials of the rank-$r$ wheel and whirl base polytopes, as well as every convex combination of the two, have $2r-2$ distinct negative roots. Their coefficient sequences are positive, unimodal, and strictly ultra log-concave of order $2r-2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40496",
  "author_total": 2,
  "authors": [
    {
      "name": "Ying Cao"
    },
    {
      "name": "Houshan Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/crdqx89areex3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40496",
  "fulltext_url": null,
  "id": "crdqx89areex3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40496",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40496",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/crdqx89areex3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40496",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40496"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Real-rooted Ehrhart $h^*$-polynomials of crown posets and wheel and whirl matroids",
  "title_text": "Real-rooted Ehrhart h^*-polynomials of crown posets and wheel and whirl matroids",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/crdqx89areex3",
  "venue": "arXiv",
  "versions": []
}