{
  "abstract": "We prove log-concavity for the determinant-weighted external semi-activity polynomials of all real flat arrangements, strengthening their known trapezoidality. In fact, we establish a quadratic coefficient inequality that, in rank at least two, implies power concavity with an explicit rank-dependent exponent. The proof uses a new mixed-volume representation of the coefficients and the Alexandrov--Fenchel inequality. A more general formula gives a factorization and log-concavity for related mixed-volume sequences. As applications, we establish the conjectured log-concavity for spanning-tree polynomials of Eulerian digraphs, extend it to positive circulation weights, and strengthen the coefficient inequalities for Alexander polynomials of special alternating links.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33651",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuan Gao"
    },
    {
      "name": "Tianyu Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4zhe7d4dwqm9f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33651",
  "fulltext_url": null,
  "id": "4zhe7d4dwqm9f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33651",
  "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"
    ],
    [
      "arxiv",
      "math.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.33651",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4zhe7d4dwqm9f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33651",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33651"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Log-concavity of flat arrangement polynomials",
  "title_text": "Log-concavity of flat arrangement polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/4zhe7d4dwqm9f",
  "venue": "arXiv",
  "versions": []
}