{
  "abstract": "We count maximal cylinders on zero holonomy $\\mathbb{Z}$-covers of genus $2$ square-tiled surfaces, up to $\\mathbb{Z}$-action, obtaining quadratic asymptotics. We also show that the leading term of the asymptotic, called the Siegel-Veech constant, can be recovered via a large-genus approximation by intermediate finite covers. Our work applies to the infinite staircases introduced by P. Hubert and G. Weitze-Schmithüsen. For many members of this family, we explicitly compute the associated Siegel-Veech constants. In particular, we exhibit the first infinite family of examples of zero holonomy $\\mathbb{Z}$-cover in which the number of cylinders grows sub-quadratically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06609",
  "author_total": 2,
  "authors": [
    {
      "name": "Mauro Artigiani"
    },
    {
      "name": "Angel Pardo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0jmgv9xhvgqnx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06609",
  "fulltext_url": null,
  "id": "0jmgv9xhvgqnx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06609",
  "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"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7220716013",
  "pdf_url": "https://arxiv.org/pdf/2610.06609",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0jmgv9xhvgqnx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06609",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06609"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Counting Cylinders on Z-covers of Genus 2 Square-tiled Surfaces",
  "title_text": "Counting Cylinders on Z-covers of Genus 2 Square-tiled Surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/0jmgv9xhvgqnx",
  "venue": "arXiv",
  "versions": []
}