Résumé : In this talk I will introduce the framework of iterated grafting operators, an operator-based model for generating and analyzing combinatorial structures. This formalism naturally connects to partial differential equations and to the normal ordering problem in operator algebras, and provides powerful tools for enumeration. The combinatorial study of these objects was initiated by Blasiak and Flajolet in Philippe Flajolet’s last article Combinatorial Models of Creation–Annihilation, but many aspects remain unexplored.

I will then focus on two specific models of preferential attachment graphs that arise from this approach. For these models, I will explain how to extract asymptotics from the associated generating functions using analytic techniques. Finally, I will discuss bijective correspondences with these graphs and open perspectives for random generation.

Dernière modification : Tuesday 30 September 2025

Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr