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.