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

Author

William P. Orrick, Nov 08 2005

Keywords

• nonn
• hard

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

• 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.

Extensions

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

Edited by William P. Orrick, Dec 20 2011