A129732
Number of main classes of Graeco-Latin squares of order n. That is, species of pairs of orthogonal Latin squares.
Original entry on oeis.org
1, 1, 1, 0, 7, 2165, 91846374
Offset: 3
The unique example for n=3 has two Latin squares [[0, 2, 1], [2, 1, 0], [1, 0, 2]] and [[0, 2, 1], [1, 0, 2], [2, 1, 0]].
A072377
Number of pairs of orthogonal Latin squares of order n.
Original entry on oeis.org
1, 0, 36, 3456, 3110400, 0, 3131834388480000, 32162058365970677760000, 19083454070548282639185346560000
Offset: 1
More terms (and corrected the degenerate first term) from
Ian Wanless, Dec 22 2015
A266171
Number of reduced maximal pairs of orthogonal Latin squares.
Original entry on oeis.org
0, 0, 1, 0, 0, 0, 341880, 7832534400, 7188529229970480
Offset: 1
A266177
Number of species of bachelor Latin squares.
Original entry on oeis.org
0, 1, 0, 1, 1, 12, 141, 281633, 18922355489
Offset: 1
- J. Egan and I. M. Wanless, Enumeration of MOLS of small order, Mathematics of Computation 85, 2016, 799-824.
- A. B. Evans, Latin squares without orthogonal mates, Des. Codes Cryptog. 40 (2006), 121-130.
- I. M. Wanless and B. S. Webb, The existence of latin squares without orthogonal mates, Des. Codes Cryptogr., 40 (2006), 131-135.
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