Power series with positive coefficients arising from the characteristic   polynomials of positive matrices
  Let A be an nxn (entrywise) positive matrix and let f(t)=det(I-t A). We prove that there always exists a positive integer N such that 1-f(t)^{1/N} has positive coefficients. 
Thomas J. Laffey, Raphael Loewy, Helena \v{S}migoc
math.SP