Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A construction of integer-valued polynomials with prescribed sets of
  lengths of factorizations   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}.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin