{
  "abstract": "We classify all 1024 length-two mesh patterns on involutions into exactly 287 equidis- tribution classes, consisting of 262 trivial classes and 25 nontrivial classes. Since many bi- jections on arbitrary permutations do not preserve the involution condition, our proofs use several involution-preserving bijections, including conjugation and local adjacent-transposition operations, transposition of the RSK recording tableau, prefix-rank swap bijections and marked-occurrence bijections. In particular, we establish the equidistribution of INV-099, a nontrivial class closely related to the unrestricted Class 69, by adapting the marked- occurrence bijection of Zhang and Zhao through a symmetric closure of the marked set. We also obtain explicit distribution formulas and recurrences for several classes, including continued fractions obtained by specializing known labeled Motzkin-path formulas and rational expressions derived from paired skew decompositions of involutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33028",
  "author_total": 2,
  "authors": [
    {
      "name": "Xinyu Su"
    },
    {
      "name": "Philip B. Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c36whcmng2606.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33028",
  "fulltext_url": null,
  "id": "c36whcmng2606",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33028",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223830758",
  "pdf_url": "https://arxiv.org/pdf/2610.33028",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c36whcmng2606.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33028",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33028"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Equidistribution of mesh patterns of length 2 on involutions",
  "title_text": "Equidistribution of mesh patterns of length 2 on involutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/c36whcmng2606",
  "venue": "arXiv",
  "versions": []
}