{
  "abstract": "In this note we prove $\\mathrm{forb}(n,\\mathbf{1}_{r-2}\\times C_4)=Θ(n^{r-1/2})$, thus providing a series of counterexamples of a 2005 conjecture of the first two authors. Here $\\mathbf{1}_{r-2}\\times C_4$ is the $r$-extension of the 4-cycle, that is the $r$-uniform hypergraph of four edges obtained by joining a set of $r-2$ vertices to each edge of $C_4$. $\\mathrm{forb}(n,F)$ is the largest number of edges of a simple hypergraph $G$ on $n$ vertices without \\emph{trace} (induced subhypergraph) $F$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13987",
  "author_total": 3,
  "authors": [
    {
      "name": "Richard P. Anstee"
    },
    {
      "name": "Attila Sali"
    },
    {
      "name": "Pei Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4cqbn9hfkx647.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13987",
  "fulltext_url": null,
  "id": "4cqbn9hfkx647",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13987",
  "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": "W7221760612",
  "pdf_url": "https://arxiv.org/pdf/2610.13987",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4cqbn9hfkx647.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.13987",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13987"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Forbidding $r$-extension of $C_4$ -- a counterexample of the Anstee-Sali conjecture",
  "title_text": "Forbidding r-extension of C_4 -- a counterexample of the Anstee-Sali conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/4cqbn9hfkx647",
  "venue": "arXiv",
  "versions": []
}