{
  "abstract": "Let $M$ be a binary matroid of rank $r$ with no $F_7$-minor, and let $B_M^\\star$ denote the maximum of its basis-generating polynomial over nonnegative weights of total mass $r$. We prove the sharp inequality $B_M^\\star\\leq 2^r/(r+1)$, with equality holding if and only if the nonloop simplification of $M$ is $M(K_{r+1})$. Binary matroids with no $F_7$-minor also form the largest minor-closed class of matroids on which this inequality holds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14370",
  "author_total": 1,
  "authors": [
    {
      "name": "Haozhou Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/54tw7zkrr5sd1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14370",
  "fulltext_url": null,
  "id": "54tw7zkrr5sd1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14370",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7221810815",
  "pdf_url": "https://arxiv.org/pdf/2610.14370",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/54tw7zkrr5sd1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14370",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14370"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Sharp Basis-Mass Inequality for Binary Matroids without a Fano Minor",
  "title_text": "A Sharp Basis-Mass Inequality for Binary Matroids without a Fano Minor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/54tw7zkrr5sd1",
  "venue": "arXiv",
  "versions": []
}