Factorization of integer-valued polynomials with square-free denominator

Abstract

We describe an algorithm to compute the essentially different factorizations of a given image primitive integer-valued polynomial $f(X)=g(X)/d\in\Q[X]$, where $g\in \mathbb{Z}[X]$ and $d\in \mathbb{N}$ is square-free, assuming that the factorization of $g(X)$ in $\mathbb{Z}[X]$ and $d$ in $\mathbb{Z}$ is known. We translate this problem into a combinatorial one.

accepted by Communications in Algebra. revised edition: minor changes in the organization of the sections of the paper. (no. pages: 16)

References in corpus (2)

• A construction of integer-valued polynomials with prescribed sets of lengths of factorizations
• Primary decomposition of the ideal of polynomials whose fixed divisor is divisible by a prime power

Cited by in corpus (5)

• Non-absolutely irreducible elements in the ring of Integer-valued polynomials
• A Survey on Fixed Divisors
• Characterizing absolutely irreducible integer-valued polynomials over discrete valuation domains
• Irreducibility of integer-valued polynomials I
• Irreducible integer-valued polynomials with prescribed minimal power that factors non-uniquely