A construction of integer-valued polynomials with prescribed sets of lengths of factorizations

Abstract

For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n irreducibles in Int(Z)={g in Q[x] | g(Z) contained in Z}.

To appear in Monatshefte für Mathematik; 11 pages

References in corpus (1)

• Non-unique factorization of polynomials over residue class rings of the integers

Cited by in corpus (11)

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• Power monoids: A bridge between Factorization Theory and Arithmetic Combinatorics
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• Semigroup rings as weakly Krull domains
• Absolute irreducibility of the binomial polynomials
• Factorization of integer-valued polynomials with square-free denominator
• 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
• Irreducible integer-valued polynomials with prescribed minimal power that factors non-uniquely