cp's OEIS Frontend

A087982 Maximal permanent of a nonsingular n X n (+1,-1)-matrix.

%I A087982 #22 Feb 22 2020 16:15:11
%S A087982 1,0,2,8,24,128
%N A087982 Maximal permanent of a nonsingular n X n (+1,-1)-matrix.
%C A087982 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).
%C A087982 This has been proved by Budrevich and Guterman. - _Sergei Shteiner_, Jan 21 2020
%C A087982 The maximal possible value for the permanent of a singular n X n (+1,-1)-matrix is obviously n!.
%H A087982 Mikhail V. Budrevich, Alexander E. Guterman, <a href="https://arxiv.org/abs/1810.04439">Kräuter conjecture on permanents is true</a>, arXiv:1810.04439 [math.CO], 2018.
%H A087982 Arnold R. Kräuter and Norbert Seifter, <a href="http://dx.doi.org/10.1080/03081088408817591">Some properties of the permanent of (1,-1)-matrices</a>, Linear and Multilinear Algebra 15 (1984), 207-223.
%H A087982 Norbert Seifter, <a href="http://dx.doi.org/10.1007/BF02760525">Upper bounds for permanents of (1,-1)-matrices</a>, Israel J. Math. 48 (1984), 69-78.
%H A087982 Edward Tzu-Hsia Wang, <a href="http://dx.doi.org/10.1007/BF02760844">On permanents of (1,-1)-matrices</a>, Israel J. Math. 18 (1974), 353-361.
%H A087982 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%F A087982 a(n) = A087981(n-1) for n >= 5. - _Sergei Shteiner_, Jan 20 2020
%e A087982 a(4) = 8 from the following matrix:
%e A087982 -1 +1 +1 +1
%e A087982 +1 +1 +1 +1
%e A087982 +1 -1 +1 -1
%e A087982 -1 +1 +1 -1
%Y A087982 For n != 4 this is given by A087981. Cf. A087983.
%K A087982 nonn
%O A087982 1,3
%A A087982 _N. J. A. Sloane_, Oct 28 2003
%E A087982 a(4) = 8 from _W. Edwin Clark_ and _Wouter Meeussen_, a(5) = 24 and a(6) = 128 from _Jaap Spies_, Oct 29 2003