Title:Enumerating planar stuffed maps as hypertrees of mobiles
| Speaker | Nathan Pagliaroli |
| Affiliation | University of Waterloo |
| Location | MC 6029 |
Abstract: A planar stuffed map is an embedding of a graph into the 2-sphere, considered up to orientation-preserving homeomorphisms, such that the complement of the graph is a collection of disjoint topologically connected components that are each homeomorphic to the 2-sphere with multiple boundaries. This is a generalization of planar maps whose complement of the graph is a collection of disjoint topologically connected components that are each homeomorphic to a disc. In this talk I will outline my work in constructing a bisection between bipartite planar stuffed maps and collections of integer-labelled trees connected by hyperedges such that they form a hypertree. This bijection directly generalizes the Bouttier-Di Franceso-Guitter bijection between bipartite planar maps and mobiles. Additionally, we show that the generating functions of these trees of mobiles satisfy both an algebraic equation, generalizing the case of ordinary planar maps, and a new functional equation. As an example, we explicitly enumerate a class of stuffed quadrangulations.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.