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 A087982 Maximal permanent of a nonsingular n X n (+1,-1)-matrix. 3
 1, 0, 2, 8, 24, 128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS It is conjectured by Kraeuter and Seifter that for n >= 5 the maximal permanent of a nonsingular n X n (+1,-1)-matrix is attained by a matrix with exactly n-1 -1's on the diagonal (compare A087981). This has been proved by Budrevich and Guterman. - Sergei Shteiner, Jan 21 2020 The maximal possible value for the permanent of a singular n X n (+1,-1)-matrix is obviously n!. LINKS Mikhail V. Budrevich, Alexander E. Guterman, Kräuter conjecture on permanents is true, arXiv:1810.04439 [math.CO], 2018. Arnold R. Kräuter and Norbert Seifter, Some properties of the permanent of (1,-1)-matrices, Linear and Multilinear Algebra 15 (1984), 207-223. Norbert Seifter, Upper bounds for permanents of (1,-1)-matrices, Israel J. Math. 48 (1984), 69-78. Edward Tzu-Hsia Wang, On permanents of (1,-1)-matrices, Israel J. Math. 18 (1974), 353-361. FORMULA a(n) = A087981(n-1) for n >= 5. - Sergei Shteiner, Jan 20 2020 EXAMPLE a(4) = 8 from the following matrix: -1 +1 +1 +1 +1 +1 +1 +1 +1 -1 +1 -1 -1 +1 +1 -1 CROSSREFS For n != 4 this is given by A087981. Cf. A087983. Sequence in context: A123775 A052624 A272590 * A176475 A145238 A093458 Adjacent sequences:  A087979 A087980 A087981 * A087983 A087984 A087985 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 28 2003 EXTENSIONS a(4) = 8 from W. Edwin Clark and Wouter Meeussen, a(5) = 24 and a(6) = 128 from Jaap Spies, Oct 29 2003 STATUS approved

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Last modified September 21 13:20 EDT 2020. Contains 337272 sequences. (Running on oeis4.)