Examples for the range of its application are various lattice walk models, enumeration of parking functions (or equivalently, hashing with linear probing), and the Potts-q random matrix model.
In this series of lectures, we will present the kernel method in its various disguises, along with pedagogical examples for each of these. We shall examine the question of whether the generating functions obtained are rational, algebraic, differentiably finite, or neither. Naturally, this has important consequences for the singularity structure of the generating functions, and therefore for the asymptotic behaviour of its coefficients.
We will further highlight applicability of competing methods. Finally, if time permits, we shall also consider counting problems leading toq-deformations.