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 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 Algebra 15 (1984), 207-223.

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