

A215645


Depth for {+1,1} maximal determinant matrices: minimal depth for which a proper submatrix is also a maximal determinant matrix.


0



1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 3, 5, 6, 7, 8, 8, 1, 7, 10, 10, 10
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OFFSET

1,8


COMMENTS

The complementary depth m(A) of a maximal determinant {+1,1} matrix of order n is the maximum m < n such that a maximal determinant matrix of order m occurs as a proper submatrix of A, or 0 if n = 1. The depth d(A) of A is d(A) := n  m(A). The depth d(n) is the minimum of d(A) over all maximal determinant matrices A of order n.
We calculated the first 21 terms of the sequence by an exhaustive computation of minors of known maximal determinant matrices as of August 2012.


LINKS



EXAMPLE

For n = 11 the depth is 3 because there is a maximal determinant matrix of order 11 that has a maximal determinant submatrix of order 8 = 113, but no larger proper maximal determinant submatrices. Note that only one of the three Hadamard equivalence classes of maximal determinant matrices of order 11 gives depth 3; the others give depth 4, but we take the minimum.


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



STATUS

approved



