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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 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..21.

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


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.


Cf. A003432, A003433, A013588.

Sequence in context: A074077 A078381 A118975 * A288777 A087724 A152047

Adjacent sequences:  A215641 A215642 A215643 * A215645 A215646 A215647




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


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



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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)