{
  "abstract": "We give a general principle that converts fixed-uniformity bounds for forbidden traces into bounds with polynomial dependence on the uniformity. More precisely, let $H$ be a fixed set system on $h\\ge1$ vertices, and suppose that, for some $α\\ge0$, $\\operatorname{ex}_j(m,\\operatorname{Tr}(H))=O_{H,j}(m^α)$ for every fixed integer $j\\ge1$. Then, for every $\\varepsilon>0$, there is a constant $C_{H,α,\\varepsilon}$ such that \\[ \\operatorname{ex}_r(m,\\operatorname{Tr}(H)) \\le C_{H,α,\\varepsilon} r^{h-1-α+\\varepsilon}m^α\\] for all $m\\ge r\\ge2$. In particular, for trace-$C_4$-free hypergraphs and every $\\varepsilon>0$ there is a constant $C_\\varepsilon$ such that \\[ \\operatorname{ex}_r(m,\\operatorname{Tr}(C_4)) \\le C_\\varepsilon r^{3/2+\\varepsilon}m^{3/2} \\] for all $m\\ge r\\ge2$. We also construct trace-$C_4$-free $r$-graphs showing that \\[ \\operatorname{ex}_r(m,\\operatorname{Tr}(C_4)) \\ge c r^{1/2}m^{3/2} \\] for an absolute constant $c>0$, for every fixed $r\\ge3$ and all sufficiently large $m$ (depending on $r$).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08151",
  "author_total": 1,
  "authors": [
    {
      "name": "Pei Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ap4h4x7ty1px.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08151",
  "fulltext_url": null,
  "id": "2ap4h4x7ty1px",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08151",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7221043080",
  "pdf_url": "https://arxiv.org/pdf/2610.08151",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ap4h4x7ty1px.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08151",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08151"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Polynomial-in-$r$ bounds for forbidden traces of uniform hypergraphs",
  "title_text": "Polynomial-in-r bounds for forbidden traces of uniform hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/2ap4h4x7ty1px",
  "venue": "arXiv",
  "versions": []
}