This material has been published in Electronic J. Combin. 18(1) (2011), Article P152, 16 pp, the only definitive repository of the content that has been certified and accepted after peer review.

Roland Bacher and Christian Krattenthaler

Chromatic statistics for Catalan and Fuß-Catalan numbers

(12 pages)

Abstract. 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 formula.

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