Permutative universal realizability

A list of complex numbers is said to be , if it is the spectrum of a nonnegative matrix. In this paper we provide a new sufficient condition for a given list to be (UR), that is, realizable for each possible Jordan canonical form allowed by . Furthermore, the resulting matrix (that is explicity provided) is permutative, meaning that each of its rows is a permutation of the first row. In particular, we show that a real Suleĭmanova spectrum, that is, a list of real numbers having exactly one positive element, is UR by a permutative matrix.