{
  "abstract": "The Tutte polynomial is a fundamental invariant of graphs and matroids. For a matroid M of rank r, the Tutte polynomial T_M(x,y) of M serves as a generalization of the characteristic polynomial chi_M(x), with the relationship given by chi_M(x) = (-1)^r T_M(1-x,0). For any real number t satisfying 0 <= t <= 1, under suitable exclusion hypotheses on M, we establish an upper bound on the coefficients of the polynomial T_M(x,t) (resp., T_M(t,y)) in terms of girth g and the number of circuits of size g (resp., maximum cardinality h of hyperplanes and the number of hyperplanes of size h). The resulting characteristic polynomial bound extends the bound of Delaplane and Wu [Discrete Math. 312(12-13) (2012) 2062-2068] to simple U_{g-1,g+1}-free matroids satisfying n >= r + c_g, thereby giving a partial affirmative answer to the question of extending their upper bound beyond binary matroids.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34985",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuxin Liu"
    },
    {
      "name": "Weihua Yang"
    },
    {
      "name": "Xiaxia Guan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4hjs3mhv97hk2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34985",
  "fulltext_url": null,
  "id": "4hjs3mhv97hk2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34985",
  "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": "W7223791370",
  "pdf_url": "https://arxiv.org/pdf/2610.34985",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4hjs3mhv97hk2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34985",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34985"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Upper bounding the coefficients of Tutte polynomials with a variable fixed",
  "title_text": "Upper bounding the coefficients of Tutte polynomials with a variable fixed",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/4hjs3mhv97hk2",
  "venue": "arXiv",
  "versions": []
}