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Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2011

Chromatic statistics for triangulations and Fu{ß}-Catalan complexes

Roland Bacher

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.

Dates et versions

hal-00612650 , version 1 (29-07-2011)

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Roland Bacher, Christian Krattenthaler. Chromatic statistics for triangulations and Fu{ß}-Catalan complexes. The Electronic Journal of Combinatorics, 2011, 18, pp.#P152. ⟨hal-00612650⟩

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