{
  "abstract": "By the Marcus-Tardos Theorem (formerly the Stanley-Wilf Conjecture), every permutation class other than the class of all permutations has a finite upper growth rate, meaning that the $n$th root of the number of permutations of length $n$ in the class has a finite limit superior. It has long been conjectured that this limit superior is in fact always a proper limit. We disprove this by constructing a permutation class whose upper and lower growth rates differ. The construction uses grid classes with cubic row-column graphs of increasing girth, obtained from Haar graphs of finite 2-groups. The corresponding hereditary property of ordered graphs also disproves an analogous 2006 conjecture of Balogh, Bollobás, and Morris. Along the way, we show that every proper permutation class with a D-finite generating function has a proper growth rate. We also establish refined enumerative bounds for grid classes, which lead to a short proof of Albert and Vatter's generalization of Bevan's Theorem on the growth rates of grid classes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30369",
  "author_total": 2,
  "authors": [
    {
      "name": "Jay Pantone"
    },
    {
      "name": "Vincent Vatter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2g9e7e975h2c8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30369",
  "fulltext_url": null,
  "id": "2g9e7e975h2c8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30369",
  "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",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223274085",
  "pdf_url": "https://arxiv.org/pdf/2610.30369",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2g9e7e975h2c8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30369",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30369"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Permutation classes need not have proper growth rates",
  "title_text": "Permutation classes need not have proper growth rates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/2g9e7e975h2c8",
  "venue": "arXiv",
  "versions": []
}