Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On tropical dualities in cluster algebras   We study two families of integer vectors playing a crucial part in the
structural theory of cluster algebras: the $\gg$-vectors parameterizing cluster
variables, and the $\cc$-vectors parameterizing the coefficients. We prove two
identities relating these vectors to each other. The proofs depend on the
sign-coherence assumption for $\cc$-vectors that still remains unproved in full
generality.

14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph