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.

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