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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)
 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 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. 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 A087724 A152047 Adjacent sequences:  A215641 A215642 A215643 * A215645 A215646 A215647 KEYWORD nonn,hard,more AUTHOR Richard P. Brent and Judy-anne 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

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