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. © 2013 Foundation Compositio Mathematica.
Linear independence of cluster monomials for skew-symmetric cluster algebras
Labardini Fragoso, D.;
2013
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. © 2013 Foundation Compositio Mathematica.
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