Transitive Sets of Mutually Orthogonal Latin Squares
Combinatorics
2026-02-02 v1 Discrete Mathematics
Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2601.22205,
title = {Transitive Sets of Mutually Orthogonal Latin Squares},
author = {Amadou Keita and Ilya Shapiro},
journal= {arXiv preprint arXiv:2601.22205},
year = {2026}
}
Comments
25 pages