On a refinement of the generalized Catalan numbers for Weyl groups

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Cyclic Sieving of Noncrossing Partitions for Complex Reflection Groups (2007, methodology): “When p = h+ 1, these W -orbits W\Q/(h+ 1)Q in the finite torus Q/(h+ 1)Q counted in the last formula are known (by work of Athanasiadis [4] and of Cellini, Papi, et al; see Armstrong [1, §1.”
Enumerative properties of generalized associahedra (2004, unknown): “a y, (27) which is known to coincide with the h-vector for all root systems, see [1, 2, 4].”
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (2006, background): “The first is the theory of “nonnesting partitions”, whose Fuss-Catalan version is due to Athanasiadis [4, 5]; the second is the theory of cluster complexes, whose Fuss-Catalan version is due to Fomin and Reading [61].”
Root systems and generalized associahedra (2005, background): “9 is a combination of results in [2, 19, 39, 44, 48]; see [2] for a historical overview, and for further generalizations.”
Generalized cluster complexes and Coxeter combinatorics (2005, unknown): “…the complexes ∆ m (Φ) provide natural generalizations of the Fuss-Catalan, Kirkman-Cayley, and Przytycki-Sikora numbers to arbitrary types, suggesting connections with a host of well studied problems in the algebraic combinatorics of ﬁnite Coxeter groups, root systems, and hyperplane arrangements.”