On the properties of the exchange graph of a cluster algebra
arXiv:math/0703151
Abstract
We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra $\A$ in two cases: when $\A$ is of geometric type and when $\A$ is arbitrary and its exchange matrix is nondegenerate. In the second case we also prove that the exchange graph does not depend on the coefficients of $\A$. Both conjectures were formulated recently by Fomin and Zelevinsky.
arXiv commentFormer Conjecture 2 split into Conjectures 2 and 3. Former Theorem 3 split into Theorems 4 and 5 accordingly. Former Section 2 split into Sections 2 and 3 accordingly. An error in the proof of case (i) of the former Theorem 3 (now Theorem 4) corrected, see 10 lines after equation (12)