We study Galton-Watson branching processes conditioned on the total progeny to be n which are scaled by a sequence cn tending to infinity as o( p n). It is shown that this process weakly converges to the totallocal time of a two-sided three-dimensional Bessel process. This is done by means of characteristic functions and a generating function approach. 1.

Given a class of combinatorial structures C, we consider the quantity N(n; m), the number of multiset constructions P (of C) of size n having exactly m C-components. Under general

We consider random mappings from an n--element set into itself with constraints on coalescence as introduced by Arney and Bender. A local limit theorem for the distribution of the number of predecessors of a random point in such a mapping is presented by using a generating function approach and singularity analysis. 1.

We derive asymptotic results on the distribution of the number of descendants in simply generated trees. Our method is based on a generating function approach and complex contour integration. 1.