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