#####
Séminaire Lotharingien de Combinatoire, B10g (1984).

[Formerly: Publ. I.R.M.A. Strasbourg, 1987, 340/S-10, p.
117-118.]

# Norbert Seifter

# Obere Schranken für die Permanente von (1,-1)-Matrizen

**Abstract.**
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 *n*x*n* (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
Algebra **15**
(1984), 207-223.

Norbert Seifter, *Upper bounds for permanents of*
(1,-1)-*matrices*,
Israel J. Math. **48** (1984), 69-78.