#####
Séminaire Lotharingien de Combinatoire, B50f (2004), 19 pp.

# Helmut Prodinger

# The Kernel Method: A Collection of Examples

**Abstract.**
The kernel method has recently become quite popular. Roughy speaking,
in certain cases one obtains for a multivariate generating function
a functional equation. For certain couplings of the variables, the denominator
vanishes, but since one knows a priori that a power series expansion exists,
one concludes that the numerator must also vanish. This is sufficient to
compute the generating function, at least at special values, and subsequently
in general.
We present a collection of examples where this technique works. All of them
have a certain random walk flavour.

Received: June 17, 2003.
Revised: April 28, 2004.
Accepted: May 5, 2004.
Final Version: May 13, 2004.

The following versions are available: