{
  "abstract": "A plane hypermap with a boundary is a connected graph embedded in the plane with a distinguished face, and whose inner faces are properly face-bicolored. We say that such hypermaps are k-alternating if the colors of the faces adjacent to the distinguished face alternate at most 2k times when going counterclockwise. Eynard and Orantin, in [EO2005], have found a universal expression for the generating functions of k-alternating hypermaps as a surprisingly simple function of the generating function of 1-alternating hypermaps. In this article, we will provide combinatorial formulas for k-alternating hypermaps using specific subclasses of hypermaps in which each vertex can either be connected to a previously marked vertex, called accessible, or connected to all other vertices in what we call a blob. In particular, this method will allow us to derive the results from [EO2005] from a combinatorial perspective, and we anticipate that it will lead to the computation of asymptotics for hypermaps in future work. This article is naturally a sequel to, and most importantly a generalization of, the results in [BEL26], which deals essentially with the case of 1- and 2-alternating hypermaps.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01148",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Lejeune"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dc5z39rdv086z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01148",
  "fulltext_url": null,
  "id": "dc5z39rdv086z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01148",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01148",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dc5z39rdv086z.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01148",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01148"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Enumeration of plane hypermaps with a mixed boundary II",
  "title_text": "Enumeration of plane hypermaps with a mixed boundary II",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/dc5z39rdv086z",
  "venue": "arXiv",
  "versions": []
}