... (Theorems 1.1, 1.2, 2.1, and 2.2) present refinements of the plain enumeration of triangulations and Fuß–Catalan complexes arising from certain vertex-colourings of triangulations and Fuß–Catalan complexes, ... inversion formula [8] Finally, Section is devoted to the proof of Theorem 2.2, and thus also of Theorem 1.2, which it generalises 1.3 3-Coloured triangulations In the sequel, Pn stands for a convex ... a b a a b c b c c a b c Figure 1: All 3-coloured triangulations for n = 0, 1, 2, Our first result provides a closed formula for the number of triangulations with a fixed colour distribution of...