Properties of Random Triangulations and Trees

Let Tn denote the set of triangulations of a convex polygon K with n sides. We study functions that measure very natural "geometric" features of a triangulation Tn, for example n() which counts the maximal number of diagonals in incident to a single vertex of K. It is familiar that Tn is bijectively equivalent to Bn, the set of rooted binary trees with n - 2 internal nodes, and also to Pn, the set of non-negative lattice paths that start at 0, make 2n - 4 steps Xi of size

• Type: Journal
• Year: 1999
• Where: DCG
• Authors: Luc Devroye, Philippe Flajolet, Ferran Hurtado, Marc Noy, William L. Steiger
• Keywords: Convex Polygon, DCG 1999, Non-negative Lattice Paths, Triangulation Tn