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A301371
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Maximum determinant of an n X n matrix with n copies of the numbers 1 .. n.
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3
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OFFSET
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0,3
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COMMENTS
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27296640 <= a(8) <= 27583339 (upper bound from Gasper's determinant theorem).
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LINKS
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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
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EXAMPLE
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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)
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CROSSREFS
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Cf. A085000.
Sequence in context: A067302 A212599 A052182 * A115415 A065058 A032031
Adjacent sequences: A301368 A301369 A301370 * A301372 A301373 A301374
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KEYWORD
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nonn,hard,more
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AUTHOR
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Hugo Pfoertner, Mar 21 2018
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STATUS
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approved
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