Transitive Sets of Mutually Orthogonal Latin Squares
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915761910448128 |
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| author | Keita, Amadou Shapiro, Ilya |
| author_facet | Keita, Amadou Shapiro, Ilya |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_22205 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transitive Sets of Mutually Orthogonal Latin Squares Keita, Amadou Shapiro, Ilya Combinatorics Discrete Mathematics Group Theory 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. |
| title | Transitive Sets of Mutually Orthogonal Latin Squares |
| topic | Combinatorics Discrete Mathematics Group Theory |
| url | https://arxiv.org/abs/2601.22205 |