Geodesic
Chromatic statistics for triangulations and Fuß-Catalan complexes
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/639
Classification : 05A15, 05A19
Mots-clés : Catalan number, Fuß-Catalan number, triangulation, Fuß-Catalan complex, barycentric subdivision, Schlegel diagram, vertex colouring, simplicial complex, Lagrange-Good inversion formula 
@article{10_37236_639,
     author = {R. Bacher and C. Krattenthaler},
     title = {Chromatic statistics for triangulations and {Fu{\ss}-Catalan} complexes},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/639},
     zbl = {1227.05032},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/639/}
}
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R. Bacher; C. Krattenthaler. Chromatic statistics for triangulations and Fuß-Catalan complexes. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/639

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