A180087 Upper bound for the determinant of a matrix whose entries are a permutation of 1, ..., n^2.

1, 11, 450, 41021, 6865625, 1867994210, 762539814814, 441077015225642, 346335386150480625, 357017114947987625629, 470379650542113331346272, 774869480550211708169959725, 1566955892015559322525350178004

Offset: 1

Author

Hugo Pfoertner, Aug 09 2010

Keywords

• nonn

References

• 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.

Links

• Rainer Rosenthal, Table of n, a(n) for n = 1..191
• O. Gasper, H. Pfoertner and M. Sigg, An Upper Bound for the Determinant of a Matrix with given Entry Sum and Square Sum JIPAM, vol. 10, Iss. 3, art. 63, 2008.
• Markus Sigg, Gasper's determinant theorem, revisited, arXiv:1804.02897 [math.CO], 2018.

Crossrefs

a(n) is an upper bound for A085000(n).

Formula

a(n) = floor(sqrt(3*((n^5+n^4+n^3+n^2)/12)^n*(n^2+1)/(n+1))).