{
  "abstract": "The enumeration of pattern-avoiding permutations has been a popular area of study over the past several decades, but comparatively little attention has been given to the topic of pattern-avoiding involutions. In this paper, we derive the algebraic generating functions of two Wilf-equivalence classes of involutions avoiding a single pattern of length $4$, $\\operatorname{Av^I}(2431)$ and $\\operatorname{Av^I}(3421)$. We then adapt the Mosaic method, a fast counting algorithm for permutations, to count involutions and apply it to substantially extend the known initial terms of the counting sequences for the remaining two Wilf-equivalence classes avoiding a pattern of length $4$, $\\operatorname{Av^I}(1324)$ and $\\operatorname{Av^I}(4231)$. Based on these extended sequences, we empirically analyze the asymptotic behavior of the counting sequences of these two classes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04352",
  "author_total": 3,
  "authors": [
    {
      "name": "Christian Bean"
    },
    {
      "name": "Anthony J. Guttmann"
    },
    {
      "name": "Jay Pantone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3nwqat0j2295.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04352",
  "fulltext_url": null,
  "id": "e3nwqat0j2295",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04352",
  "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": "W7211865900",
  "pdf_url": "https://arxiv.org/pdf/2609.04352",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3nwqat0j2295.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04352",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04352"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Enumerating Pattern-Avoiding Involutions using Combinatorial Exploration",
  "title_text": "Enumerating Pattern-Avoiding Involutions using Combinatorial Exploration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/e3nwqat0j2295",
  "venue": "arXiv",
  "versions": []
}