Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compatible associative products and trees   We compute dimensions of graded components for free algebras with two
compatible associative products, and give a combinatorial interpretation of
these algebras in terms of planar rooted trees.

36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ