This material has been published in
J. Combin. 18(1) (2011), Article P152, 16 pp,
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and Christian Krattenthaler
Chromatic statistics for Catalan and Fuß-Catalan numbers
We refine Catalan numbers and Fuß-Catalan numbers by introducing
colour statistics for triangulations of polygons
and d-dimensional generalisations
thereof which we call Fuß-Catalan complexes.
Our refinements consist in showing that the number of triangulations,
respectively Fuß-Catalan complexes, with a given colour distribution
of its vertices is given by closed product formulae.
The crucial ingredient in the proof is the Lagrange-Good inversion
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