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A307164
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Maximum number of intercalates in a diagonal Latin square of order n.
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9
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OFFSET
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1,4
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COMMENTS
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An intercalate is a 2 X 2 subsquare of a Latin square.
a(10) >= 101, a(11) >= 94, a(12) >= 252, a(13) >= 156, a(14) >= 353. - Eduard I. Vatutin, May 31 2021, updated Sep 10 2023
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LINKS
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Eduard Vatutin, Alexey Belyshev, Natalia Nikitina, and Maxim Manzuk, Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10, High-Performance Computing Systems and Technologies in Sci. Res., Automation of Control and Production (HPCST 2020), Communications in Comp. and Inf. Sci. book series (CCIS, Vol. 1304) Springer, Cham (2020), 127-146.
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EXAMPLE
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One of the best known diagonal Latin squares of order n=5
0 1 2 3 4
4 2 0 1 3
1 4 3 2 0
3 0 1 4 2
2 3 4 0 1
has 4 intercalates:
. . 2 3 . . . . . . . . . . . . . . . .
. . . . . . . 0 . 3 . . . . . . . . . .
. . 3 2 . . . 3 . 0 1 . 3 . . . 4 3 . .
. . . . . . . . . . 3 . 1 . . . . . . .
. . . . . . . . . . . . . . . . 3 4 . .
so a(5)=4. (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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