On Numbers of Pseudo-Triangulations∗

We study the maximum numbers of pseudo-triangulations and pointed pseudo-triangulations that can be embedded over a specific set of points in the plane or con-tained in a specific triangulation. We derive the bounds O(5.45N) and Ω(2.41N) for the maximum number of pointed pseudo-triangulations that can be contained in a specific triangulation over a set of N points. For the number of all pseudo-triangulations contained in a triangulation we derive the bounds O∗(6.54N) and Ω(3.30N). We also prove that O∗(89.1N) pointed pseudo-triangulations can be embedded over any specific set of N points in the plane, and at most 120N general pseudo-triangulations.