Vol. 38, No. 1, 1971

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Counterexamples to a conjecture of G. N. de Oliveira

Darald Joe Hartfiel

Vol. 38 (1971), No. 1, 67–68
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
Authors
Darald Joe Hartfiel