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A299784
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Maximal size of a main class for diagonal Latin squares of order n with the first row in ascending order.
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6
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1, 0, 0, 2, 4, 96, 192, 1536, 1536, 15360, 15360, 184320, 184320, 2580480, 2580480
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OFFSET
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1,4
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COMMENTS
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a(n) <= 2^m * m! * 4, where m = floor(n/2).
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LINKS
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E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Supercomputing Days Russia 2018, Moscow, Moscow State University, 2018, pp. 933-942.
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FORMULA
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EXAMPLE
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From Eduard I. Vatutin, May 30 2021: (Start)
The following DLS of order 9 has a main class with cardinality 1536:
0 1 2 3 4 5 6 7 8
1 2 0 4 8 6 5 3 7
7 4 5 8 0 3 2 6 1
5 8 7 6 1 0 3 2 4
8 0 3 2 7 1 4 5 6
3 7 8 5 6 4 1 0 2
6 3 1 7 5 2 8 4 0
2 6 4 0 3 8 7 1 5
4 5 6 1 2 7 0 8 3
The following DLS of order 10 has a main class with cardinality 15360:
0 1 2 3 4 5 6 7 8 9
1 2 0 4 5 3 9 8 6 7
3 5 6 1 8 7 4 0 9 2
9 4 7 8 3 2 1 6 0 5
2 7 3 0 9 8 5 1 4 6
6 8 5 9 2 4 7 3 1 0
4 6 9 7 0 1 3 2 5 8
7 0 4 6 1 9 8 5 2 3
8 3 1 5 6 0 2 9 7 4
5 9 8 2 7 6 0 4 3 1
(End)
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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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