Factorization of Integer-Valued Polynomials with Square-Free Denominator

We describe an algorithm to compute the different factorizations of a given image primitive integer-valued polynomial f(X) = g(X)/d ∈ ?X], where g ∈ ?X] and d ∈ ? is square-free, assuming that the factorizations of g(X) in ?X] and d in ? are known. We translate this problem into a combinatorial one.