Chromatic statistics for Catalan and Fuß-Catalan numbers
Copyright policy )Chromatic statistics for Catalan and Fuß-Catalan numbers
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.
AmS-LaTeX, 16 pages; minor changes; final journal version
- MEDIZINISCHE UNIVERSITAT GRAZ Austria
- Joseph Fourier University France
- Grenoble Alpes University France
- French National Centre for Scientific Research France
- Institut Fourier France
101029 Mathematische Statistik, FOS: Mathematics, Mathematics - Combinatorics, 05A15 (Primary), 05A19 (Secondary), 101029 Mathematical statistics, Combinatorics (math.CO)
101029 Mathematische Statistik, FOS: Mathematics, Mathematics - Combinatorics, 05A15 (Primary), 05A19 (Secondary), 101029 Mathematical statistics, Combinatorics (math.CO)
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