{
  "abstract": "We establish a new asymptotic lower bound for the volume of a maximal partial Room square of even order $n$. We prove that its volume is at least $\\frac{2\\sqrt{66}-6}{57}n^2-O(n)$, improving the leading coefficient $1/8$ in the lower bound obtained by Meszka and Rosa. The proof combines two counting arguments, one based on a transversal of empty cells and the other on the graph of occurring symbol pairs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07117",
  "author_total": 2,
  "authors": [
    {
      "name": "Peter Horak"
    },
    {
      "name": "Dongryul Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9s37f4pq1x7bc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07117",
  "fulltext_url": null,
  "id": "9s37f4pq1x7bc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07117",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07117",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9s37f4pq1x7bc.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07117",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07117"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An improved lower bound for maximal partial Room squares",
  "title_text": "An improved lower bound for maximal partial Room squares",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/9s37f4pq1x7bc",
  "venue": "arXiv",
  "versions": []
}