Chromatic statistics for Catalan and Fuß-Catalan numbers
arXiv:1101.1416
Abstract
We refine Catalan numbers and Fuß-Catalan numbers by introducing colour statistics for triangulations of polygons and -dimensional generalisations there-of 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.
AmS-LaTeX, 16 pages; minor changes; final journal version