{
  "abstract": "We prove that the Füredi-Hajnal limit and the Stanley-Wilf limit of a uniformly random permutation matrix of order $k$ are at most $\\exp\\bigl(O(\\sqrt{k}(\\log k)^{5/2})\\bigr)$ with probability tending to one as $k\\to\\infty$. This improves the bound $\\exp\\bigl(O(k^{2/3}(\\log k)^{7/3}/(\\log\\log k)^{1/3})\\bigr)$ of Cibulka and Kynčl. Together with the lower bound due to Fox, these bounds show that the logarithms of both limits are $k^{1/2+o(1)}$ for almost all permutations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02707",
  "author_total": 1,
  "authors": [
    {
      "name": "Jesse Geneson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/akqz8zn333vqy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02707",
  "fulltext_url": null,
  "id": "akqz8zn333vqy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02707",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7220357589",
  "pdf_url": "https://arxiv.org/pdf/2610.02707",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/akqz8zn333vqy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02707",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02707"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Typical growth of the Füredi-Hajnal and Stanley-Wilf limits",
  "title_text": "Typical growth of the Füredi-Hajnal and Stanley-Wilf limits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/akqz8zn333vqy",
  "venue": "arXiv",
  "versions": []
}