Mathematics – Combinatorics
Scientific paper
2011-01-07
Electronic J. Combin. 18(1) (2011), Article #P152
Mathematics
Combinatorics
AmS-LaTeX, 16 pages; minor changes; final journal version
Scientific paper
We refine Catalan numbers and Fu{\ss}-Catalan numbers by introducing colour statistics for triangulations of polygons and $d$-dimensional generalisations there-of which we call Fu{\ss}-Catalan complexes. Our refinements consist in showing that the number of triangulations, respectively Fu{\ss}-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.
Bacher Roland
Krattenthaler Christian
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