Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functional equations in polynomials   We determine all F,G in C[X] of degree at least 2 for which the semigroup
generated by F and G under composition is not the free semigroup on the letters
F and G. We also solve the same problem for F,G in X^2 C[[X]], and prove
partial analogues over arbitrary fields.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics