Consider the following problem: for S a subset of Z^2, we want
to count the plane lattice walks with steps in S, that start from (0,0)
and always remain in the first quadrant. This enumerative combinatorics
problem is extremely hard, and still an active research topic. In this
talk, I will first give a gentle introduction to the use of generating
functions in enumerative combinatorics. Afterwards, I will treat one
particular case of this problem, which will shed some light on the
formidable richness of the tools used in its study.
