{
  "abstract": "The Tutte polynomial is a bivariate polynomial that has been extensively studied in graph and matroid theory. Gordon was the first to study the Tutte polynomial $T(P;x,y)$ of the greedoid induced by a poset $P$, including the special case of series-parallel posets. In particular, Gordon and McMahon conjectured that, for any two series-parallel posets $P$ and $Q$, the equality $T(P;x,y)=T(Q;x,y)$ holds if and only if $P\\cong Q$. In studying this conjecture, Gordon introduced a subclass $\\mathcal{P}$ of series-parallel posets and proved that this equivalence holds for all $P,Q\\in\\mathcal{P}$. In this paper, we introduce a new subclass $\\mathrm H$ of series-parallel posets and prove that $\\mathcal P\\subseteq\\mathrm H$. Moreover, we show that, for every $P\\in\\mathrm H$ and every $Q\\in\\mathrm{SP}$, the equality $T(P;x,y)=T(Q;x,y)$ holds if and only if $P\\cong Q$, thereby extending Gordon's result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27524",
  "author_total": 3,
  "authors": [
    {
      "name": "Jianxuan Luo"
    },
    {
      "name": "Tingzeng Wu"
    },
    {
      "name": "Hong-Jian Lai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0ch03y34hd51.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27524",
  "fulltext_url": null,
  "id": "f0ch03y34hd51",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27524",
  "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": "W7214152724",
  "pdf_url": "https://arxiv.org/pdf/2609.27524",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0ch03y34hd51.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27524",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27524"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the Tutte polynomial of series-parallel posets",
  "title_text": "On the Tutte polynomial of series-parallel posets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/f0ch03y34hd51",
  "venue": "arXiv",
  "versions": []
}