Enumeration of geometric configurations on a convex polygon

We survey recent work on the enumeration of non-crossing configurations on the set of vertices of a convex polygon, such as triangulations, trees, forests and other configurations. Exact formulae and limit laws are determined for several parameters of interest. In the second part of the talk we present results on the enumeration of chord diagrams (pairings of 2n vertices of a convex polygon by means of n disjoint pairs). We present limit laws for the number of components, the size of the largest component and the number of crossings.

(Joint work with Philippe Flajolet and other authors.)