{
  "abstract": "Dunshee and Ellingham recently showed that seven natural properties of a cellularly embedded graph form a Fano-plane framework. We establish an analogous framework for binary delta-matroids. For a binary delta-matroid $D$ and $τ$, let $Z_3(D,τ)$ denote its associated binary tight $3$-matroid. The six outer points are represented by evenness or bipartiteness of $D$ and its global vertex-flip transforms. For the seventh point, we call $D$ $Z_3$-bipartite when every circuit of $Z_3(D,τ)$ has even cardinality. We show that the satisfied properties are precisely the nonzero vectors of a subspace of $\\Ftwo^3$. For ribbon-graphic delta-matroids, $Z_3$-bipartiteness is equivalent to bipartiteness of the medial graph, so the construction recovers the Fano-plane framework for embedded graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08588",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhuo Li"
    },
    {
      "name": "Xian'an Jin"
    },
    {
      "name": "Qi Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fqcjzx8a1w822.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08588",
  "fulltext_url": null,
  "id": "fqcjzx8a1w822",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08588",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7212010931",
  "pdf_url": "https://arxiv.org/pdf/2609.08588",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fqcjzx8a1w822.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08588",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08588"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Fano framework for binary delta-matroids",
  "title_text": "A Fano framework for binary delta-matroids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/fqcjzx8a1w822",
  "venue": "arXiv",
  "versions": []
}