Metraipolis › archive › dc_23ba67b99db7

Latin Squares with Few Transversals — arXiv:2609.08624

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.08624
License (as archived): CC0-1.0
Archived: 2026-10-16T14:49:01.903Z
SHA-256 of the archived text: 0de2f8892bb1a471473a26003f976d1241d3d5ed056b22fcd22243be6620c48f
Stable URL of this page: https://metraipolis.com/documento/dc_23ba67b99db7

How to cite

Latin Squares with Few Transversals — arXiv:2609.08624 — arXiv (en), https://arxiv.org/abs/2609.08624 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_23ba67b99db7 (Metraipolis archive dc_23ba67b99db7, sha256 0de2f8892bb1a471473a26003f976d1241d3d5ed056b22fcd22243be6620c48f)

BibTeX

@misc{dc23ba67b99db7,
  title = {Latin Squares with Few Transversals — arXiv:2609.08624},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.08624},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_23ba67b99db7; sha256 0de2f8892bb1a471473a26003f976d1241d3d5ed056b22fcd22243be6620c48f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.08624. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.08624 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T14:32:29.863Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).