{
  "abstract": "Oxley conjectured that a matroid with a circuit-cocircuit intersection of size $k\\geq 4$ has one of size $k-2$. Using the standard polynomial representation of the classical extended binary Golay code, we construct an identically self-dual binary matroid of rank $12$ on $24$ elements. Its circuit-cocircuit intersection sizes are exactly $0,2,4,6,8$, and $12$, disproving the conjecture for $k=12$. The proof is self-contained and does not rely on the full weight distribution of the code or on an enumeration of all circuits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06033",
  "author_total": 1,
  "authors": [
    {
      "name": "Houshan Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0dv4y5jsn88jf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06033",
  "fulltext_url": null,
  "id": "0dv4y5jsn88jf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06033",
  "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": "W7220670001",
  "pdf_url": "https://arxiv.org/pdf/2610.06033",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0dv4y5jsn88jf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06033",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06033"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A counterexample to the circuit-cocircuit intersection conjecture",
  "title_text": "A counterexample to the circuit-cocircuit intersection conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/0dv4y5jsn88jf",
  "venue": "arXiv",
  "versions": []
}