In Speyer and Thomas's work, Acyclic Cluster Algebras Revisited the characteristics of $c$-vectors of cluster algebras with the $B$-matrix of the initial seed acyclic are given in Theorem 1.4. Do we have similar results for acyclic cluster algebra in general (i.e. The $B$-matrix of some seed is acyclic but the $B$-matrix of the original seed might not)?
In particular I'm interested in the case where the original $B$-matrix is induced by the cyclic quiver of $n$ vertices.
