Séminaire Lotharingien de Combinatoire, B50f (2004), 19 pp.
The Kernel Method: A Collection of Examples
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
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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