{
  "abstract": "The number of transversals in a Latin square $L(G)$ whose rows and columns are indexed by a finite group $G$ has been determined computationally for all $G$ of order at most $23$ and for $C_{25}$. However, computation of the number of transversals of $L(G)$ has until now been considered intractable for all non-cyclic groups $G$ of order $32$. We show, for a group $G$ containing an order $2$ normal subgroup $N$, that the image of a transversal in $L(G)$ under the quotient mapping from $G$ to $G/N$ is a $2$-plex in $L(G/N)$. We then derive linear algebraic conditions that determine the number of transversals in $L(G)$ whose image under the quotient mapping is a given $2$-plex in $L(G/N)$. This allows us to count transversals in $L(G)$ by examining all $2$-plexes in $L(G/N)$. Although we can simplify the counting of $2$-plexes in $L(G/N)$ by taking advantage of their symmetry group, the linear algebraic conditions can vary over a symmetry class of $2$-plexes. However, in the case that $G$ takes the splitting form $C_2 \\times H$, the linear algebraic conditions become invariant over each symmetry class and so the counting of transversals in $L(C_2 \\times H)$ reduces to counting the $2$-plexes in $L(H)$ under the action of their symmetry group. We illustrate the power of these techniques by computing the exact number of transversals in $L(C_2^5)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35611",
  "author_total": 4,
  "authors": [
    {
      "name": "James A. Davis"
    },
    {
      "name": "Jonathan Jedwab"
    },
    {
      "name": "Ian M. Wanless"
    },
    {
      "name": "Amy Wiebe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58bhnatc43wjh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35611",
  "fulltext_url": null,
  "id": "58bhnatc43wjh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35611",
  "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": "W7223832016",
  "pdf_url": "https://arxiv.org/pdf/2610.35611",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58bhnatc43wjh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35611",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35611"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counting transversals in Latin squares over groups of even order",
  "title_text": "Counting transversals in Latin squares over groups of even order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/58bhnatc43wjh",
  "venue": "arXiv",
  "versions": []
}