Chromatic statistics for Catalan and Fuß-Catalan numbers [article]

Roland Bacher, Christian Krattenthaler
2011 arXiv   pre-print
We refine Catalan numbers and Fuß-Catalan numbers by introducing colour statistics for triangulations of polygons and d-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.
arXiv:1101.1416v2 fatcat:7ycqvl5tyjff5m736fgyklioyi