Cluster algebras and symmetrizable matrices

Abstract

In this paper, we study combinatorial properties of quasi-Cartan companions defined by the c-vectors of acyclic skew-symmetrizable cluster algebras. In particular, we show that the diagram of any skew-symmetrizable matrix associated with an acyclic cluster algebra has an admissible cut of edges.

5 pages. arXiv admin note: text overlap with arXiv:1201.4270