{
  "abstract": "A permutation is $n$-universal if it contains every permutation of length $n$ as a pattern. We prove that a uniformly random permutation of length $32n^2$ is $n$-universal with probability at least $1-\\exp(-c n/\\log n)$, for an absolute constant $c>0$ and all sufficiently large $n$. This removes a $\\log\\log n$ factor from an earlier result of He and Kwan~\\cite{He-Kwan} and resolves an open problem of Alon~\\cite{Alon2016}. The proof was found by GPT-6 Pro.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13530",
  "author_total": 2,
  "authors": [
    {
      "name": "Yu Chen"
    },
    {
      "name": "Yiting Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e8e477r4f444b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13530",
  "fulltext_url": null,
  "id": "e8e477r4f444b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13530",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7221553281",
  "pdf_url": "https://arxiv.org/pdf/2610.13530",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e8e477r4f444b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13530",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13530"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Quadratic-size Random Permutations are Universal",
  "title_text": "Quadratic-size Random Permutations are Universal",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/e8e477r4f444b",
  "venue": "arXiv",
  "versions": []
}