A construction of integer-valued polynomials with prescribed sets of lengths of factorizations
Rings and Algebras
2014-09-04 v3
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}.
Cite
@article{arxiv.1112.5753,
title = {A construction of integer-valued polynomials with prescribed sets of lengths of factorizations},
author = {Sophie Frisch},
journal= {arXiv preprint arXiv:1112.5753},
year = {2014}
}
Comments
To appear in Monatshefte f\"ur Mathematik; 11 pages