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{\bf R. Bacher and C. Krattenthaler}
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{\bf Chromatic Statistics for Triangulations and Fu{\ss}--Catalan Complexes}
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We introduce Fu\ss--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.

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