Groupe de travail "Transcendance et combinatoire"

On the algebraicity of solutions of functional equations with one catalytic variable (part I)

by Mr Hadrien Notarantonio (INRIA Saclay)

Amphi Darboux (Institut Henri Poincaré )

Amphi Darboux

Institut Henri Poincaré

11 Rue Pierre et Marie Curie, 75005 Paris

ABSTRACT: Functional equations with one catalytic variable naturally appear in enumerative combinatorics (e.g. when counting planar maps, walks,...). The relevant solution of such an equation is a formal power series with polynomial coefficients in what is called the catalytic variable. Classifying the nature of this solution (e.g. algebraic, D-finite,...) has been an important topic of research since the 60's, starting with the works of Brown and Tutte. In 2006, Bousquet-Mélou and Jehanne obtained a general theorem giving the algebraicity of those solutions. In this talk, I will start by introducing those equations before stating and proving the result of Bousquet-Mélou and Jehanne.

Organized by

Alin Bostan, Lucia Di Vizio, Kilian Raschel