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A279649
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Rows of the self-orthogonal Latin squares of order 8, lexicographically sorted.
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5
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1, 2, 3, 4, 5, 6, 7, 8, 3, 4, 1, 2, 6, 5, 8, 7, 4, 5, 7, 3, 8, 2, 1, 6, 6, 7, 5, 8, 3, 1, 2, 4, 7, 1, 4, 6, 2, 8, 5, 3, 5, 8, 6, 7, 1, 3, 4, 2, 8, 3, 2, 5, 4, 7, 6, 1, 2, 6, 8, 1, 7, 4, 3, 5, 1, 2, 3, 4, 5, 6, 7, 8, 3, 4, 1, 2, 6, 5, 8, 7, 4, 5, 8, 3, 7, 2, 6, 1, 6, 8, 5, 7, 3, 1, 4, 2, 8, 1, 4, 6, 2, 7, 3, 5, 5, 7, 6, 8, 1, 3, 2, 4, 2, 6, 7, 1, 8, 4, 5, 3, 7, 3, 2, 5, 4, 8, 1, 6
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OFFSET
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1,2
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COMMENTS
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An m X m Latin square consists of m sets of the numbers 1 to m arranged in such a way that no row or column contains the same number twice.
Two m X m Latin squares are orthogonal if no pair of corresponding elements occurs more than once.
A self-orthogonal Latin square is a Latin square that is orthogonal to its transpose.
There are 4180377600 self-orthogonal Latin squares of order 8.
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LINKS
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EXAMPLE
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The first four squares are:
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
3 4 1 2 6 5 8 7 3 4 1 2 6 5 8 7 3 4 1 2 6 5 8 7 3 4 1 2 6 5 8 7
4 5 7 3 8 2 1 6 4 5 8 3 7 2 6 1 4 6 7 3 2 8 1 5 4 6 8 3 2 7 5 1
6 7 5 8 3 1 2 4 6 8 5 7 3 1 4 2 5 7 6 8 1 3 2 4 5 8 6 7 1 3 4 2
7 1 4 6 2 8 5 3 8 1 4 6 2 7 3 5 6 8 5 7 3 1 4 2 6 7 5 8 3 1 2 4
5 8 6 7 1 3 4 2 5 7 6 8 1 3 2 4 7 1 4 5 8 2 6 3 8 1 4 5 7 2 3 6
8 3 2 5 4 7 6 1 2 6 7 1 8 4 5 3 8 3 2 6 7 4 5 1 2 5 7 1 4 8 6 3
2 6 8 1 7 4 3 5 7 3 2 5 4 8 1 6 2 5 8 1 4 7 3 6 7 3 2 6 8 4 1 5
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CROSSREFS
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KEYWORD
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nonn,fini,tabf
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AUTHOR
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STATUS
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approved
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