Effective Asymptotics of Combinatorial Systems

In their book “Analytic Combinatorics”, Flajolet and Sedgewick describe a general approach that starts from a combinatorial description, translates this description into equations satisfied by generating functions, views these generating functions as analytic functions and exploits their singular behavior to deduce asymptotic properties of the combinatorial objects when their size becomes large.

With Bruno Salvy, we developed computational tools that automate large parts of this approach and in this talk I will outline the main steps.