5 papers · 1 filter
Enumeration of maps with tight boundaries and the Zhukovsky transformation
Jérémie Bouttier, Emmanuel Guitter, Grégory Miermont
We consider maps with tight boundaries, i.e. maps whose boundaries have minimal length in their homotopy class, and discuss the properties of their generating functions $T^{(g)}_{\…
The slice decomposition of planar hypermaps
Marie Albenque, Jérémie Bouttier
The slice decomposition is a bijective method for enumerating planar maps (graphs embedded in the sphere) with control over face degrees. In this paper, we extend the slice decompo…
Enumeration of planar bipartite tight irreducible maps
Jérémie Bouttier, Emmanuel Guitter, Hugo Manet
We consider planar bipartite maps which are both tight, i.e. without vertices of degree , and -irreducible, i.e. such that each cycle has length at least and such that…
On quasi-polynomials counting planar tight maps
Jérémie Bouttier, Emmanuel Guitter, Grégory Miermont
A tight map is a map with some of its vertices marked, such that every vertex of degree is marked. We give an explicit formula for the number of plana…
Multicritical Schur measures and higher-order analogues of the Tracy-Widom distribution
Dan Betea, Jérémie Bouttier, Harriet Walsh
We introduce multicritical Schur measures, which are probability laws on integer partitions which give rise to non-generic fluctuations at their edge. They are in the same universa…