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.
