Résumé : During the last 20 years, integrable hierarchies (KP/Toda) have proven to be a great source of recurrence formulas for maps of all kinds. However, most of those formulas still lack a bijective explication. In this talk, we provide a bijective proof for the planar case of Louf's formula, which counts bipartite planar maps with prescribed face degrees and arises from the Toda hierarchy. We actually show that his formula hides two simpler formulas, both of which can be rewritten as natural equations on trees using duality and Schaeffer's bijection for eulerian maps. The underlying bijection for trees can also be interpreted directly on bipartite maps as " slit-slide-sew " operations. As far as we know, this is the first bijection for a formula arising from an integrable hierarchy with infinitely many parameters

 [vidéo]

Dernière modification : Wednesday 21 May 2025

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