

A215644


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


1



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

1,3


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..21.
R. P. Brent, The Hadamard Maximal Determinant Problem
Richard P. Brent and Judyanne H. Osborn, On minors of maximal determinant matrices, arXiv:1208.3819, 2012.
Index entries for sequences related to maximal determinants


EXAMPLE

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.


CROSSREFS

Cf. A003432, A003433, A013588.
Sequence in context: A074077 A078381 A118975 * A288777 A343503 A087724
Adjacent sequences: A215641 A215642 A215643 * A215645 A215646 A215647


KEYWORD

nonn,hard,more


AUTHOR

Richard P. Brent and Judyanne Osborn, Aug 18 2012


EXTENSIONS

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


STATUS

approved



