A111368 - OEIS

%I #12 Sep 29 2017 06:10:10

%S 1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,5,3,3,3,3,7

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

%C 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.

%H R. P. Brent, W. P. Orrick, J. Osborn, and P. Zimmermann, <a href="https://arxiv.org/abs/1112.4160">Maximal determinants and saturated D-optimal designs of orders 19 and 37</a>, arXiv:1112.4160 [math.CO], 2011.

%H J. H. E. Cohn, <a href="https://doi.org/10.1016/0097-3165(94)90063-9">On the number of D-optimal designs</a>, J. Combin. Theory Ser. A 66 (1994) 214-225.

%H W. P. Orrick, <a href="https://arxiv.org/abs/math/0511141">On the enumeration of some D-optimal designs</a>, arXiv:math/0511141 [math.CO], 2005-2006.

%H W. P. Orrick and B. Solomon, <a href="http://www.indiana.edu/~maxdet">The Hadamard maximal determinant problem</a>

%H Warren D. Smith, <a href="https://dl.acm.org/citation.cfm?id=915627">Studies in Computational Geometry Motivated by Mesh Generation</a>, Ph. D. dissertation, Princeton University (1988).

%H E. Spence, <a href="http://www.maths.gla.ac.uk/~es/">Ted Spence's home page</a>, website.

%H J. Williamson, <a href="http://www.jstor.org/stable/2306240">Determinants whose elements are 0 and 1</a>, Amer. Math. Monthly 53 (1946), 427-434. Math. Rev. 8,128g.

%Y Cf. A003433, A007299.

%K nonn,hard

%O 1,11

%A _William P. Orrick_, Nov 08 2005

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

%E Edited by _William P. Orrick_, Dec 20 2011