Judy-anne Osborn - cp's OEIS frontend

User: Judy-anne Osborn

Judy-anne Osborn has authored 2 sequences.

A215645 Depth for {+1,-1} maximal determinant matrices: minimal depth for which a proper submatrix is also a maximal determinant matrix.

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

Offset: 1

Richard P. Brent and Judy-anne Osborn, Aug 18 2012

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.

			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 = 11-3, 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.

R. P. Brent, The Hadamard Maximal Determinant Problem
Richard P. Brent and Judy-anne H. Osborn, On minors of maximal determinant matrices, arXiv:1208.3819, 2012.

Cf. A003432, A003433, A215644.

A215644 Full spectrum threshold for maximal determinant {+1, -1} matrices: largest order of submatrix for which the full spectrum of absolute determinant values occurs.

Original entry on oeis.org

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

Offset: 1

Richard P. Brent and Judy-anne Osborn, Aug 18 2012

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.

			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.

R. P. Brent, The Hadamard Maximal Determinant Problem
Richard P. Brent and Judy-anne H. Osborn, On minors of maximal determinant matrices, arXiv:1208.3819, 2012.
Index entries for sequences related to maximal determinants

Cf. A003432, A003433, A013588.

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

cp's OEIS Frontend

User: Judy-anne Osborn

A215645 Depth for {+1,-1} maximal determinant matrices: minimal depth for which a proper submatrix is also a maximal determinant matrix.

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