Linear independence of cluster monomials for skew-symmetric cluster algebras
arXiv:1203.1307
Abstract
Fomin-Zelevinsky conjectured that in any cluster algebra, the cluster monomials are linearly independent and that the exchange graph and cluster complex are independent of the choice of coefficients. We confirm these conjectures for all skew-symmetric cluster algebras.
14 pages. v2: Bibliography expanded. v3: Added results 3.7, 3.8, 4.7, 4.8 and 5.6. v4: Added reference and minor changes