

A087982


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


3




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 n1 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

Table of n, a(n) for n=1..6.
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), 207223.
Norbert Seifter, Upper bounds for permanents of (1,1)matrices, Israel J. Math. 48 (1984), 6978.
Edward TzuHsia Wang, On permanents of (1,1)matrices, Israel J. Math. 18 (1974), 353361.
Index entries for sequences related to binary matrices


FORMULA

a(n) = A087981(n1) 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



