A111368 The number of maximal determinant {-1,1} matrices of order n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 5, 3, 3, 3, 3, 7

Offset

1,11

Comments

The number of inequivalent maximal determinant {-1,1} matrices of order n where two matrices are considered equivalent if one can be obtained from the other by permuting rows, permuting columns and multiplying rows or columns by -1. Additional terms: a(24)=60, a(25)=78, a(28)=487. The terms a(4n) are given in sequence A007299.

Links

Table of n, a(n) for n=1..21.

R. P. Brent, W. P. Orrick, J. Osborn, and P. Zimmermann, Maximal determinants and saturated D-optimal designs of orders 19 and 37, arXiv:1112.4160 [math.CO], 2011.

J. H. E. Cohn, On the number of D-optimal designs, J. Combin. Theory Ser. A 66 (1994) 214-225.

W. P. Orrick, On the enumeration of some D-optimal designs, arXiv:math/0511141 [math.CO], 2005-2006.

W. P. Orrick and B. Solomon, The Hadamard maximal determinant problem

Warren D. Smith, Studies in Computational Geometry Motivated by Mesh Generation, Ph. D. dissertation, Princeton University (1988).

E. Spence, Ted Spence's home page, website.

J. Williamson, Determinants whose elements are 0 and 1, Amer. Math. Monthly 53 (1946), 427-434. Math. Rev. 8,128g.

Crossrefs

Cf. A003433, A007299.

Sequence in context: A371884 A079724 A289357 * A140750 A028264 A208673

Adjacent sequences: A111365 A111366 A111367 * A111369 A111370 A111371

Keyword

nonn,hard

Author

William P. Orrick, Nov 08 2005

Extensions

Added a(19)-a(21) and Brent et al. reference.

Edited by William P. Orrick, Dec 20 2011

Status

approved