Reducible Rational Fractions of the type of Gaussian Polynomials with only Non-Negative Coefficients

Abstract

The following problem arose in connection with the study of Poincaré polynomials for homogeneous spaces. Letgi hi positive integers and set d = (h1, h1,…, hk), the greatest common divisors of the exponents in the denominator. Let hi = dri and assume that the ri′s are comprime in pairs, i.e.