{
  "abstract": "Let $t(n)$ denote the minimum number of transversals in a Latin square of odd order $n$. Improving upon a recent bound of Dai, Divoux and Kelly, we prove that for every $n$ such that $n \\equiv 3 \\pmod 6$, \\[ t(n) \\leq \\left( \\left(1+o(1)\\right) \\frac{2n}{3e^2}\\right)^n . \\] Our proof is based on a family of $3 \\times 3$ block Latin squares whose transversals are constrained to either lie entirely in the diagonal blocks or avoid them altogether.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08624",
  "author_total": 1,
  "authors": [
    {
      "name": "Zur Luria"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6850hj3vpjbpm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08624",
  "fulltext_url": null,
  "id": "6850hj3vpjbpm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08624",
  "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|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7212060555",
  "pdf_url": "https://arxiv.org/pdf/2609.08624",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6850hj3vpjbpm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08624",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08624"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Latin Squares with Few Transversals",
  "title_text": "Latin Squares with Few Transversals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/6850hj3vpjbpm",
  "venue": "arXiv",
  "versions": []
}