Let W be a finite crystallographic reflection group. The generalized Catalan
number of W coincides both with the number of clusters in the cluster algebra
associated to W, and with the number of noncrossing partitions for W. Natural
bijections between these two sets are known. For any positive integer m, both
m-clusters and m-noncrossing partitions have been defined, and the cardinality
of both these sets is the Fuss-Catalan number. We give a natural bijection
between these two sets by first establishing a bijection between two particular
sets of exceptional sequences in the bounded derived category for any
finite-dimensional hereditary algebra.Comment: 25 pages: v2: added new section (section 8
