{
  "abstract": "We prove that for every integer $d \\geq 3$, there exists $α<1$ such that the maximum dimension of an $n$-element poset containing no standard example of order $d$ as an induced subposet is $\\mathcal{O}_d(n^α)$. For $d=3$, we obtain an upper bound $\\mathcal{O}(n^{2/3}\\log n)$, while we also construct a family of $S_3$-free posets with dimension $Ω(n^{1/3}/\\log n)$. The proofs were found by OpenAI's ChatGPT-6 Astra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24774",
  "author_total": 3,
  "authors": [
    {
      "name": "Jędrzej Hodor"
    },
    {
      "name": "Piotr Micek"
    },
    {
      "name": "William T. Trotter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/50whtjr6djht6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24774",
  "fulltext_url": null,
  "id": "50whtjr6djht6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24774",
  "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|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223043275",
  "pdf_url": "https://arxiv.org/pdf/2610.24774",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/50whtjr6djht6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24774",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24774"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On dimension of posets excluding a standard example",
  "title_text": "On dimension of posets excluding a standard example",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/50whtjr6djht6",
  "venue": "arXiv",
  "versions": []
}