Noncrossing partitions, Bruhat order, and the cluster complex

Abstract. Among Catalan families, noncrossing partitions are especially interesting because of their poset structure. We refine it by distinguishing two kinds of cover relations, then taking the transitive closure give two new orders, with various interesting properties. We will explain the connection with the Bruhat order, then with the cluster complex.

This is joint work with Philippe Biane.