Factorizations in Int(D) where D is a Dedekind domain with infinitely...

Non-unique factorization of elements into irreducibles has been observed in the ring of integer-valued polynomials and its generalizations.  We show that all finite (multi-)sets of natural numbers greater than 1 occur as (multi-)sets of lengths of a polynomial in $\mathrm{Int}(D)$ where $D$ is a Dedekind domain with infinitely many maximal ideals all of whose residue fields are finite. In this talk, we speak about the construction techniques and consequences.