{
  "abstract": "Motivated by Gal's conjecture, Ferroni and Higashitani conjectured that the $h^*$-polynomial of any Gorenstein lattice polytope admitting a quadratic triangulation is $γ$-positive. Together with conjectures predicting quadratic properties of toric ideals of smooth lattice polytopes, this suggests that smooth Gorenstein lattice polytopes should have $γ$-positive $h^*$-polynomials. In this paper, we prove that the Ehrhart polynomial of the polar dual of every pseudo-symmetric simplicial reflexive polytope is magic positive. For pseudo-symmetric smooth Fano polytopes, we prove the stronger statement that all magic coefficients are strictly positive. Consequently, for every pseudo-symmetric simplicial reflexive polytope, its polar dual is Ehrhart positive and has a real-rooted and $γ$-positive $h^*$-polynomial. We also prove that the Ehrhart polynomial of the polar dual of the symmetric edge polytope of every cycle is magic positive. This gives an affirmative answer to a question of Konoike, who had previously proved partial positivity results for this family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06419",
  "author_total": 2,
  "authors": [
    {
      "name": "Hidefumi Ohsugi"
    },
    {
      "name": "Akiyoshi Tsuchiya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/689tnvha07sr1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06419",
  "fulltext_url": null,
  "id": "689tnvha07sr1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06419",
  "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": "W7220691618",
  "pdf_url": "https://arxiv.org/pdf/2610.06419",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/689tnvha07sr1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06419",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06419"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Magic positivity for polar duals of pseudo-symmetric smooth Fano polytopes",
  "title_text": "Magic positivity for polar duals of pseudo-symmetric smooth Fano polytopes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/689tnvha07sr1",
  "venue": "arXiv",
  "versions": []
}