We study the maximum num
bers of pseudo-triangulations and
pointed pseudo-triangulations that can
be em
bedded over a specific set of points in the plane or contained in a specific triangulation.
We derive the bounds and 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 and . We also prove that pointed pseudo-triangulations can be embedded over any specific set of N points in the plane, and at most general pseudo-triangulations.