# Counting triangulations of some
classes of subdivided convex polygons

### (26 pages)

**Abstract.**
We compute the number of triangulations of a convex *k*-gon
each of whose sides is subdivided by *r*-1 points.
We find explicit formulas and generating functions,
and we determine the asymptotic behaviour of these numbers
as *k* and/or *r* tend to infinity.
We connect
these results with the question of finding
the planar set of points in general position
that has the minimum possible number of triangulations -
a well-known open problem from computational geometry.

The following versions are available:

Back to Christian Krattenthaler's
home page.