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A301371 Maximum determinant of an n X n matrix with n copies of the numbers 1 .. n. 3
1, 1, 3, 18, 160, 2325, 41895, 961772 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

27296640 <= a(8) <= 27583339 (upper bound from Gasper's determinant theorem).

LINKS

Table of n, a(n) for n=0..7.

Ortwin Gasper, Hugo Pfoertner and Markus Sigg, An Upper Bound for the Determinant of a Matrix with given Entry Sum and Square Sum, JIPAM, Journal of Inequalities in Pure and Applied Mathematics, Volume 10, Issue 3, Article 63, 2008.

Markus Sigg, Gasper's determinant theorem, revisited, arXiv:1804.02897 [math.CO]

Index entries for sequences related to maximal determinants

EXAMPLE

Matrices with maximum determinants:

a(2) = 3:

  (2  1)

  (1  2)

a(3) = 18:

  (3  1  2)

  (2  3  1)

  (1  2  3)

a(4) = 160:

  (4  3  2  1)

  (1  4  3  2)

  (3  1  4  3)

  (2  2  1  4)

a(5) = 2325:

  (5  3  1  2  4)

  (2  5  4  1  3)

  (4  1  5  3  2)

  (3  4  2  5  1)

  (1  2  3  4  5)

a(6) = 41895:

  (6  1  4  2  3  5)

  (3  6  2  1  5  4)

  (4  5  6  3  2  1)

  (5  3  1  6  4  2)

  (1  2  5  4  6  3)

  (2  4  3  5  1  6)

a(7) = 961772:

  (7  2  3  5  1  4  6)

  (3  7  6  4  2  1  5)

  (2  1  7  6  4  5  3)

  (4  5  1  7  6  3  2)

  (6  3  5  1  7  2  4)

  (5  6  4  2  3  7  1)

  (1  4  2  3  5  6  7)

CROSSREFS

Cf. A085000.

Sequence in context: A067302 A212599 A052182 * A115415 A065058 A032031

Adjacent sequences:  A301368 A301369 A301370 * A301372 A301373 A301374

KEYWORD

nonn,hard,more

AUTHOR

Hugo Pfoertner, Mar 21 2018

STATUS

approved

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Last modified June 17 07:00 EDT 2019. Contains 324183 sequences. (Running on oeis4.)