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A301370
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Maximum determinant of an n X n (0,1)-matrix that has exactly 2*n ones.
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0
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0, 2, 2, 3, 4, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64
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OFFSET
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2,2
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COMMENTS
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A proved upper bound is abs(a(n)) <= 6^(n/6), provided by Bruhn and Rautenbach. A conjectured sharper bound is abs(a(n)) <= 2^(n/3), provided by the same authors. For n=3*k, the bound is achieved by diagonally concatenating blocks ((1 1 0)(0 1 1)(1 0 1)).
The sharper bound is proved by Araujo, Balogh, and Wang in their article. See link. - Hugo Pfoertner, Nov 04 2020
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LINKS
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EXAMPLE
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a(8) = 6 because no (0,1)-matrix with 2*8 ones with a greater determinant exists than
( 1 0 0 0 0 0 0 0 )
( 0 1 0 1 0 0 0 0 )
( 0 0 1 0 1 1 0 0 )
( 0 0 0 1 0 0 1 0 )
( 0 0 0 0 1 0 0 1 )
( 0 0 0 0 0 1 0 1 )
( 0 1 0 0 0 0 1 0 )
( 0 0 1 0 0 0 0 1 )
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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