Chromatic Statistics for Triangulations and Fuß-Catalan Complexes

We introduce Fuß–Catalan complexes as $d$-dimensional generalisations of triangulations of a convex polygon. These complexes are used to refine Catalan numbers and Fuß–Catalan numbers, by introducing colour statistics for triangulations and Fuß–Catalan complexes. Our refinements consist in showing t...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 18; no. 1
Main Authors Bacher, R., Krattenthaler, C.
Format Journal Article
LanguageEnglish
Published 22.07.2011
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Summary:We introduce Fuß–Catalan complexes as $d$-dimensional generalisations of triangulations of a convex polygon. These complexes are used to refine Catalan numbers and Fuß–Catalan numbers, by introducing colour statistics for triangulations and Fuß–Catalan complexes. Our refinements consist in showing that the number of triangulations, respectively of 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.
ISSN:1077-8926
1077-8926
DOI:10.37236/639