Chromatic statistics for triangulations and Fu{ß}-Catalan complexes
Résumé
We introduce Fuß--Catalan complexes as $d$-dimensional generalisations of triangulations of a convex polygon. These complexes are used to refine Catalan numbers and Fu{ß}--Catalan numbers, by introducing colour statistics for triangulations and Fu{ß}--Catalan complexes. Our refinements consist in showing that the number of triangulations, respectively of 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.