Counterexamples to a conjecture of G. N. de Oliveira

Darald Joe Hartfiel

Vol. 38 (1971), No. 1, 67–68

DOI: 10.2140/pjm.1971.38.67

Abstract

G. N. de Oliveira gives the following coniecture.

Conjecture. Let A be an n×n doubly stochastic irreducible matrix. If n is even, then f(z) = perm(Iz − A) has no real roots; if n is odd, then f(z) = perm(Iz − A) has one and only one real root.

In this paper we give counter examples to this conjecture.

Mathematical Subject Classification 2000

Primary: 15A51

Milestones

Received: 10 July 1970

Published: 1 July 1971