Vol. 32, No. 2, 1970

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A conjecture and some problems on permanents

Graciano de Oliveira

Vol. 32 (1970), No. 2, 495–499

Let A = [aij] denote an n × n matrix and let E be the n × n identity matrix. We will designate by detA and perm A the determinant and the permanent of A respectively. The polynomial φ(z) = det(zE A) plays a fundamental role in matrix theory. Similarly we can consider the polynomial f(z) = perm (zE A) which has been object of several studies recently, particularly when A is a doubly stochastic matrix. The aim of the present paper is to give some results on the existence of matrices satisfying certain conditions involving the roots of this polynomial.

Mathematical Subject Classification
Primary: 15.20
Received: 19 March 1968
Published: 1 February 1970
Graciano de Oliveira