{
  "abstract": "Using a unified method of identifying a telescoping function for each statistic-action pair, we prove conjectures of La Croix and Roby, and of Sheridan-Rossi that various permutation statistics, such as the number of fixed points, are homomesic under Foatic actions: compositions of the Foata bijection and dihedral symmetries of one-line notation. Underlying these results is a family of bijective identities relating permutation statistics across the Foata bijection; one of them --- an unexpected invariance of the number of right-to-left minima under reverse-complement, proved by an explicit bijection --- may be of independent interest. The telescoping functions also turn out to be shared among some Foatic actions, implying that mixing certain actions still yields a constant average on closed walks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40882",
  "author_total": 1,
  "authors": [
    {
      "name": "Peter Mao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dbp64ay0j6qqk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40882",
  "fulltext_url": null,
  "id": "dbp64ay0j6qqk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40882",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40882",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dbp64ay0j6qqk.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.40882",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40882"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Foatic Homomesy",
  "title_text": "Foatic Homomesy",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/dbp64ay0j6qqk",
  "venue": "arXiv",
  "versions": []
}