arXiv Open Access 2026

Transitive Sets of Mutually Orthogonal Latin Squares

Amadou Keita Ilya Shapiro

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Abstrak

We investigate MacNeish's conjecture (known to be false in general) in the setting of what we call "transitive" Mutually Orthogonal Latin Squares (MOLS). When we restrict our attention to "simply transitive" MOLS, we find that the conjecture holds. We provide some partial results towards the transitive case, as well as the outcome of a computer search, which introduces a new construction of MOLS. In particular, we were unable to find any transitive large (conjecture-violating) sets of MOLS in the literature.

Topik & Kata Kunci

math.CO cs.DM math.GR

Penulis (2)

Amadou Keita

Ilya Shapiro

Format Sitasi

APA MLA BibTeX

Keita, A., Shapiro, I. (2026). Transitive Sets of Mutually Orthogonal Latin Squares. https://arxiv.org/abs/2601.22205

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Informasi Jurnal

Tahun Terbit: 2026
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓