Singularity analysis of generating functions given by parametric equations
Abstract：The aim of this talk is to present some new ideas on the asymptotic expansion of positive real sequences whose generating function is given by an explicit parametric equation. To provide context, I will first introduce/recall briefly some classical theory of asymptotic analysis in enumerative combinatorics. This part follows the book of Flajolet and Sedgewick. After that, I will try to explain why "having a parametric equation" defines an interesting class of generating functions, and compare it with the class of algebraic functions. Finally, I will present some methods for the analysis of these generating functions, and give two examples of application.