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A340546
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Number of main classes of diagonal Latin squares of order 2n that contain a one-plane symmetric square.
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5
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OFFSET
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1,3
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COMMENTS
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A one-plane symmetric diagonal Latin square is a vertically or horizontally symmetric diagonal Latin square (see A296060). Such diagonal Latin squares do not exist for odd orders > 1.
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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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A horizontally symmetric diagonal Latin square:
0 1 2 3 4 5
4 2 0 5 3 1
5 4 3 2 1 0
2 5 4 1 0 3
3 0 1 4 5 2
1 3 5 0 2 4
A vertically symmetric diagonal Latin square:
0 1 2 3 4 5
4 2 5 0 3 1
3 5 1 2 0 4
5 3 0 4 1 2
2 4 3 1 5 0
1 0 4 5 2 3
Both are one-plane symmetric diagonal Latin squares.
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CROSSREFS
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KEYWORD
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nonn,more,hard,bref
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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