Properties of Random Triangulations and Trees

@article{Devroye1999PropertiesOR,
  title={Properties of Random Triangulations and Trees},
  author={Luc Devroye and Philippe Flajolet and Ferran Hurtado and Marc Noy and William L. Steiger},
  journal={Discrete & Computational Geometry},
  year={1999},
  volume={22},
  pages={105-117}
}
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 τ ∈ Tn, for example ∆n(τ) which counts the maximal number of diagonals in τ 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 ±1, and end at… CONTINUE READING
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