{
  "abstract": "Let $S_g$ be the closed oriented surface of genus $g \\geq 2$, and let $Γ$ be a finite collection of closed curves on $S_g$ that fills, in the sense that its complement is a union of disks. The total number of double points of such a $Γ$ in minimal position is at least $2g-1$; we call $Γ$ minimally intersecting when equality holds. We prove that the number $N_g$ of mapping class group orbits of minimally intersecting filling curve systems satisfies $N_g \\sim 16^g (2g)!/(64π\\sqrt{2}\\, g^3)$ as $g \\to \\infty$. We also study the single-curve subproblem, in which $Γ$ consists of a single component. Every such curve is in particular a filling system, so the corresponding count $N_g^{(1)}$ satisfies $N_g^{(1)} \\leq N_g$, which improves the upper bound previously known for single filling curves. Finally, we compute $N_g$ and $N_g^{(1)}$ exactly for small genus and conjecture an asymptotic growth rate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09102",
  "author_total": 1,
  "authors": [
    {
      "name": "Sayantika Mondal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/casata7mx8fqe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09102",
  "fulltext_url": null,
  "id": "casata7mx8fqe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09102",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221045294",
  "pdf_url": "https://arxiv.org/pdf/2610.09102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/casata7mx8fqe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Asymptotic enumeration of minimally intersecting filling curve systems on closed surfaces",
  "title_text": "Asymptotic enumeration of minimally intersecting filling curve systems on closed surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/casata7mx8fqe",
  "venue": "arXiv",
  "versions": []
}