{
  "abstract": "In this paper, we determine the asymptotic number of $F$-decompositions in typical hypergraphs. More precisely, let $F$ be a non-trivial $f$-vertex $k$-graph. We show that, for all sufficiently large $n$, every $n$-vertex $F$-divisible $(n^{-ζ},h,p)$-typical $k$-graph $G$ has $n^{\\frac{f-k+o_n(1)}{|F|}|G|}$ $F$-decompositions. As an application, we asymptotically enumerate universal cycles for $k$-subsets of $[n]$, or equivalently, tight Euler tours of the complete $k$-graph $K_n^k$. For every $k\\ge2$ and all sufficiently large $n$ satisfying $k\\mid {n-1 \\choose k-1}$, the number of such universal cycles is $n^{(1-γ(n)){n \\choose k}}$, where $0<γ(n)=o_n(1)$. More generally, for $\\ell\\in[k-1]$, we show that a sufficiently typical $n$-vertex $k$-graph $G$ satisfying the corresponding divisibility condition has $n^{(k-\\ell-γ'(n))|G|}$ Euler $\\ell$-tours, where $0<γ'(n)=o_n(1)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26579",
  "author_total": 3,
  "authors": [
    {
      "name": "Danni Li"
    },
    {
      "name": "Bin Wang"
    },
    {
      "name": "Junxue Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8a1zdwxhtvt9q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26579",
  "fulltext_url": null,
  "id": "8a1zdwxhtvt9q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26579",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7223018546",
  "pdf_url": "https://arxiv.org/pdf/2610.26579",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8a1zdwxhtvt9q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26579",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26579"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Asymptotic Enumeration of $F$-decompositions in Typical Hypergraphs and of Universal Cycles",
  "title_text": "Asymptotic Enumeration of F-decompositions in Typical Hypergraphs and of Universal Cycles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/8a1zdwxhtvt9q",
  "venue": "arXiv",
  "versions": []
}