Enumeration of MOLS of small order
Copyright policy )Enumeration of MOLS of small order
We report the results of a computer investigation of sets of mutually orthogonal Latin squares (MOLS) of small order. For n ⩽ 9 n\leqslant 9 we: determine the number of orthogonal mates for each species of Latin square of order n n ; calculate the proportion of Latin squares of order n n that have an orthogonal mate, and the expected number of mates when a square is chosen uniformly at random; classify all sets of MOLS of order n n up to various different notions of equivalence. We also provide a triple of Latin squares of order 10 that is the closest to being a set of MOLS so far found.
- Monash University Australia
orthogonal mate, MOLS, Latin square, transversal, 05B15, Transversal (matching) theory, FOS: Mathematics, Mathematics - Combinatorics, Orthogonal arrays, Latin squares, Room squares, Combinatorics (math.CO), Design of statistical experiments, plex
orthogonal mate, MOLS, Latin square, transversal, 05B15, Transversal (matching) theory, FOS: Mathematics, Mathematics - Combinatorics, Orthogonal arrays, Latin squares, Room squares, Combinatorics (math.CO), Design of statistical experiments, plex
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