Description
(Poster) I will introduce a new function on the set of pairs of cluster variables, which we call it the compatibility degree (of cluster complexes). The compatibility degree which I deal with in this talk is a generalization of the ``classical" compatibility degree introduced by Fomin and Zelevinsky. The classical one defines the generalized associahedra, and it is used to give the classification of cluster algebras of finite type. Cao and Li generalized this degree to that of cluster complexes by using d-vectors. We give another generalization by using f-vectors on the basis of their studies. This is joint work with Changjian Fu.
