

A301370


Maximum determinant of an n X n (0,1)matrix that has exactly 2*n ones.


0



0, 2, 2, 3, 4, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64
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OFFSET

2,2


COMMENTS

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)).


LINKS

Table of n, a(n) for n=2..18.
Henning Bruhn, Dieter Rautenbach, Maximal determinants of combinatorial matrices, arXiv:1711.09935 [math.CO], 2017.
Markus Sigg, Gasper's determinant theorem, revisited, arXiv:1804.02897 [math.CO]


EXAMPLE

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 )


CROSSREFS

Cf. A003432, A017979, A085000.
Sequence in context: A292420 A161654 A325854 * A225482 A004056 A284334
Adjacent sequences: A301367 A301368 A301369 * A301371 A301372 A301373


KEYWORD

nonn,more


AUTHOR

Hugo Pfoertner, Mar 20 2018


STATUS

approved



