I have a question about the definition of a seed of a cluster algebra. It is said that a seed is a pair $(R, u)$, where $R$ is a quiver with $n$ vertices, $u = \{u_1, \ldots, u_n\}$ is a free generating set of the field $Q(x_1, \ldots, x_n)$, see Page 10 of the paper.
I think here $u_i$ is in terms of $x_1, \ldots, x_n$ and $u_1, \ldots, u_n$ generate $Q(x_1, \ldots, x_n)$ freely. Is this true? Thank you very much.