login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 24 13:17 EDT 2019. Contains 324325 sequences. (Running on oeis4.)