1,3

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).

The maximal possible value for the permanent of a singular n X n (+1,-1)-matrix is obviously n!.

A. R. Kraeuter and N. Seifter, Some properties of the permanent of (1,-1)-matrices, Linear and Multilinear Algebra 15 (1984), 207-223.

N. 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.

Index entries for sequences related to binary matrices

a(4) = 8 from the following matrix:

-1 +1 +1 +1

+1 +1 +1 +1

+1 -1 +1 -1

-1 +1 +1 -1

The conjecture is that for n != 4 this is given by A087981. Cf. A087983.

Sequence in context: A157005 A123775 A052624 this_sequence A145238 A093458 A088994

Adjacent sequences: A087979 A087980 A087981 this_sequence A087983 A087984 A087985

nonn

N. J. A. Sloane (njas(AT)research.att.com), Oct 28 2003

a(4) = 8 from Edwin Clark and Wouter Meeussen, a(5) = 24 and a(6) = 128 from Jaap Spies, Oct 29 2003.