A215644 - OEIS

%I #19 Sep 12 2013 14:45:10

%S 1,1,2,2,3,4,6,4,6,6,7,6,7,7,7,8,8,8,9,8,10

%N Full spectrum threshold for maximal determinant {+1, -1} matrices: largest order of submatrix for which the full spectrum of absolute determinant values occurs.

%C a(n) is the maximum of m(A) taken over all maximal determinant matrices A of order n, where m(A) is the maximum m such that the full spectrum of possible values (ignoring sign) occurs for the minors of order m of A.

%H R. P. Brent, <a href="http://wwwmaths.anu.edu.au/~brent/maxdet/">The Hadamard Maximal Determinant Problem</a>

%H Richard P. Brent and Judy-anne H. Osborn, <a href="http://arxiv.org/abs/1208.3819">On minors of maximal determinant matrices</a>, arXiv:1208.3819, 2012.

%H <a href="/index/De#determinants">Index entries for sequences related to maximal determinants</a>

%e For n = 8 we have a(8) = 4 as a Hadamard matrix of order 8 has minors of order 4 with the full spectrum of values {0,8,16} (signs are ignored) but minors of order m > 4 do not have this property.

%Y Cf. A003432, A003433, A013588.

%K nonn,hard,more

%O 1,3

%A _Richard P. Brent_ and _Judy-anne Osborn_, Aug 18 2012

%E We calculated the first 21 terms of the sequence by an exhaustive computation of minors of known maximal determinant matrices as at August 2012.