163 citations · 827 across the 46 of their papers we have counts for
21 papers · 1 filter
Distance statistics of block-weighted planar quadrangulations
Jérémie Bouttier, Emmanuel Guitter, Hugo Manet
We study random planar quadrangulations in which each block -- i.e., each simple (without multiple edges) component -- is assigned a weight . We derive an explicit expression fo…
Enumeration of plane hypermaps with a mixed boundary I
Jérémie Bouttier, Bertrand Eynard, Thomas Lejeune
Plane hypermaps are plane maps endowed with a proper coloration of their inner faces in black or white. We consider the problem of enumerating plane hypermaps with prescribed face…
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…
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)}_{\…
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…
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…
Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants
Jérémie Bouttier, Emmanuel Guitter, Grégory Miermont
We consider planar maps with three boundaries, colloquially called pairs of pants. In the case of bipartite maps with controlled face degrees, a simple expression for their generat…
Enumeration of planar constellations with an alternating boundary
Jérémie Bouttier, Ariane Carrance
A planar hypermap with a boundary is defined as a planar map with a boundary, endowed with a proper bicoloring of the inner faces. The boundary is said alternating if the colors of…
Multicritical random partitions
Dan Betea, Jérémie Bouttier, Harriet Walsh
We study two families of probability measures on integer partitions, which are Schur measures with parameters tuned in such a way that the edge fluctuations are characterized by a…
New edge asymptotics of skew Young diagrams via free boundaries
Dan Betea, Jérémie Bouttier, Peter Nejjar +1
We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Bai…
Bumping sequences and multispecies juggling
Arvind Ayyer, Jérémie Bouttier, Sylvie Corteel +2
Building on previous work by four of us (ABCN), we consider further generalizations of Warrington's juggling Markov chains. We first introduce "multispecies" juggling, which consis…
From Aztec diamonds to pyramids: steep tilings
Jérémie Bouttier, Guillaume Chapuy, Sylvie Corteel
We introduce a family of domino tilings that includes tilings of the Aztec diamond and pyramid partitions as special cases. These tilings live in a strip of of the f…
On the two-point function of general planar maps and hypermaps
Jérémie Bouttier, Éric Fusy, Emmanuel Guitter
We consider the problem of computing the distance-dependent two-point function of general planar maps and hypermaps, i.e. the problem of counting such maps with two marked points a…
A note on irreducible maps with several boundaries
J. Bouttier, E. Guitter
We derive a formula for the generating function of d-irreducible bipartite planar maps with several boundaries, i.e. having several marked faces of controlled degrees. It extends a…
On irreducible maps and slices
J. Bouttier, E. Guitter
We consider the problem of enumerating d-irreducible maps, i.e. planar maps whose all cycles have length at least d, and such that any cycle of length d is the boundary of a face o…
Constellations and multicontinued fractions: application to Eulerian triangulations
Marie Albenque, Jérémie Bouttier
We consider the problem of enumerating planar constellations with two points at a prescribed distance. Our approach relies on a combinatorial correspondence between this family of…
Planar maps and continued fractions
J. Bouttier, E. Guitter
We present an unexpected connection between two map enumeration problems. The first one consists in counting planar maps with a boundary of prescribed length. The second one consis…
Blocked edges on Eulerian maps and mobiles: Application to spanning trees, hard particles and the Ising model
J. Bouttier, P. Di Francesco, E. Guitter
We introduce Eulerian maps with blocked edges as a general way to implement statistical matter models on random maps by a modification of intrinsic distances. We show how to code t…
Combinatorics of bicubic maps with hard particles
J. Bouttier, P. Di Francesco, E. Guitter
We present a purely combinatorial solution of the problem of enumerating planar bicubic maps with hard particles. This is done by use of a bijection with a particular class of blos…
Planar maps as labeled mobiles
J. Bouttier, P. Di Francesco, E. Guitter
We extend Schaeffer's bijection between rooted quadrangulations and well-labeled trees to the general case of Eulerian planar maps with prescribed face valences, to obtain a biject…