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A340550
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Number of main classes of diagonal Latin squares of order n that contain a doubly symmetric square.
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4
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1, 0, 0, 1, 0, 0, 0, 47, 0, 0, 0
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OFFSET
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1,8
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COMMENTS
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A doubly symmetric square has symmetries in both the horizontal and vertical planes (see A292517).
Every doubly symmetric diagonal Latin square also has central symmetry. The converse is not true in general. It follows that a(n) <= A340545(n). - Eduard I. Vatutin, May 28 2021
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LINKS
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E. I. Vatutin, Special types of diagonal Latin squares, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 9-18. (in Russian)
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EXAMPLE
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An example of a doubly symmetric diagonal Latin square:
0 1 2 3 4 5 6 7
3 2 7 6 1 0 5 4
2 3 1 0 7 6 4 5
6 7 5 4 3 2 0 1
7 6 3 2 5 4 1 0
4 5 0 1 6 7 2 3
5 4 6 7 0 1 3 2
1 0 4 5 2 3 7 6
In the horizontal direction there is a one-to-one correspondence between elements 0 and 7, 1 and 6, 2 and 5, 3 and 4.
In the vertical direction there is also a correspondence between elements 0 and 1, 2 and 4, 6 and 7, 3 and 5.
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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