{
  "abstract": "Let $u_k^{(r)}(H,p)$ be the maximum, over all $k$-vertex $r$-uniform hypergraphs $F$, of the absolute difference between the number of induced copies of $F$ in $H$ and its expectation in the binomial random $r$-graph with the same number of vertices as $H$ and edge probability $p$. Let $u_k^{(r)}(n,p)$ be the minimum of $u_k^{(r)}(H,p)$ over all $n$-vertex $r$-uniform hypergraphs, and let $D_r(n,p)$ be the distance from $p\\binom nr$ to the nearest integer. For fixed $r\\ge3$, $k\\ge2r$ and $\\varepsilon>0$, the quantity $u_k^{(r)}(n,p)$ has order $\\max\\!\\left\\{D_r(n,p),p(1-p)\\right\\}n^{k-r}$ whenever $p(1-p)n^{\\lfloor r/2\\rfloor/(\\binom{2r-2}{r}-1)}\\ge\\varepsilon$. Using local moment estimates and switchings in a sparse reservoir, we construct one hypergraph with the nearest-integer edge count that controls all induced orders simultaneously.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14712",
  "author_total": 1,
  "authors": [
    {
      "name": "Chenglong Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ae6k35bfwnxze.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14712",
  "fulltext_url": null,
  "id": "ae6k35bfwnxze",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14712",
  "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"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7221786529",
  "pdf_url": "https://arxiv.org/pdf/2610.14712",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ae6k35bfwnxze.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14712",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14712"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Induced-Count Discrepancy in Uniform Hypergraphs",
  "title_text": "Induced-Count Discrepancy in Uniform Hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/ae6k35bfwnxze",
  "venue": "arXiv",
  "versions": []
}