Séminaire Lotharingien de Combinatoire, B10g (1984).
[Formerly: Publ. I.R.M.A. Strasbourg, 1987, 340/S-10, p.
Obere Schranken für die Permanente von (1,-1)-Matrizen
E. T. H. Wang posed the following problem: is there a good upper bound
for the permanent of a nonsingular (1,-1)-matrix?
We conjecture an upper bound, namely the
permanent of the nxn (1,-1)-matrix having exactly
(n-1) -1's, these -1's being on the main diagonal,
and prove that this upper
bound holds for a large class of nonsingular matrices.
Another upper bound, weaker than the above,
is deduced for the permanents of a large class of (1,-1)-matrices, some of
which are singular.
This is a report on the papers:
Arnold R. Kräuter, Norbert Seifter, Some properties
of the permanent of (1,-1)-matrices, Linear and Multilinear
Norbert Seifter, Upper bounds for permanents of
Israel J. Math. 48 (1984), 69-78.