Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positivity in coefficient-free rank two cluster algebras   Let $b,c$ be positive integers, $x_1,x_2$ be indeterminates over $\Z$ and
$x_m, m \in \mathbb Z$ be rational functions defined by
$x_{m-1}x_{m+1}=x_m^b+1$ if $m$ is odd and $x_{m-1}x_{m+1}=x_m^c+1$ if $m$ is
even. In this short note, we prove that for any $m,k \in \Z$, $x_k$ can be
expressed as a substraction-free Laurent polynomial in $\Z[x_m^{\pm
1},x_{m+1}^{\pm 1}]$. This proves Fomin-Zelevinsky's positivity conjecture for
coefficient-free rank two cluster algebras.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph