{
  "abstract": "Jackson and Tanigawa conjectured that the rigidity matroid $\\mathcal{R}^d_n$ and the hyperconnectivity matroid $\\mathcal{H}^d_n$ are the unique maximal matroids in the posets of $\\{K_{d+2}, K_{d+2,d+2}\\}$-matroids and $\\{K_{d+2},K_{d+1,d+1}\\}$-matroids, respectively. We disprove these conjectures by showing the existence of maximal matroids that are distinct from the proposed candidates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.14663",
  "author_total": 2,
  "authors": [
    {
      "name": "Denys Bulavka"
    },
    {
      "name": "Martin Tancer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e563xxa97s5vh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.14663",
  "fulltext_url": null,
  "id": "e563xxa97s5vh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.14663",
  "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": "W7164812225",
  "pdf_url": "https://arxiv.org/pdf/2606.14663",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e563xxa97s5vh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2606.14663",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.14663"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Maximal matroids and counterexamples",
  "title_text": "Maximal matroids and counterexamples",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/e563xxa97s5vh",
  "venue": "arXiv",
  "versions": []
}