Compatibility degree of cluster complexes

We introduce a new function on the set of pairs cluster variables via f-vectors, which is called compatibility degree (of complexes). The natural generalization classical introduced by Fomin and Zelevinsky. In particular, we prove that has duality property, symmetry embedding property one has. also conjecture exchangeability property. As pieces evidence this conjecture, establish for algebras rank 2, acyclic skew-symmetric algebras, arising from weighted projective lines, marked surfaces.