52 citations · 402 across the 46 of their papers we have counts for
35 papers · 1 filter
On the scaling of random Tamari intervals and Schnyder woods of random triangulations (with an asymptotic D-finite trick)
Guillaume Chapuy
We consider a Tamari interval of size (i.e., a pair of Dyck paths which are comparable for the Tamari relation) chosen uniformly at random. We show that the height of a uniform…
A telescopic proof of Cayley's formula
Guillaume Chapuy, Guillem Perarnau
We give a short proof of the fact that the number of labelled trees on vertices is . Although many short proofs are known, we have not seen this one before.
On the edge-density of the Brownian co-graphon and common ancestors of pairs in the CRT
Guillaume Chapuy
Bassino et al. (arXiv:1907.08517) have shown that uniform random co-graphs (graphs without induced ) of size converge to a certain non-deterministic graphon. The edge-dens…
Topological recursion for Orlov-Scherbin tau functions, and constellations with internal faces
Valentin Bonzom, Guillaume Chapuy, Séverin Charbonnier +1
We study the correlators arising from Orlov-Scherbin 2-Toda tau functions with rational content-weight , at arbitrary values of the two sets of time parameters. Com…
Random partitions under the Plancherel-Hurwitz measure, high genus Hurwitz numbers and maps
Guillaume Chapuy, Baptiste Louf, Harriet Walsh
We study the asymptotic behaviour of random integer partitions under a new probability law that we introduce, the Plancherel-Hurwitz measure. This distribution, which has a natural…
Enumeration of non-oriented maps via integrability
Valentin Bonzom, Guillaume Chapuy, Maciej Dołęga
In this note, we examine how the BKP structure of the generating series of several models of maps on non-oriented surfaces can be used to obtain explicit and/or efficient recurrenc…
Counting chains in the noncrossing partition lattice via the W-Laplacian
Guillaume Chapuy, Theo Douvropoulos
We give an elementary, case-free, Coxeter-theoretic derivation of the formula for the number of maximal chains in the noncrossing partition lattice of a real re…
-monotone Hurwitz numbers: Virasoro constraints, BKP hierarchy, and -BGW integral
Valentin Bonzom, Guillaume Chapuy, Maciej Dołęga
We study a -deformation of monotone Hurwitz numbers, obtained by deforming Schur functions into Jack symmetric functions. We give an evolution equation for this model and derive…
Coxeter factorizations with generalized Jucys-Murphy weights and Matrix Tree theorems for reflection groups
Guillaume Chapuy, Theo Douvropoulos
We prove universal (case-free) formulas for the weighted enumeration of factorizations of Coxeter elements into products of reflections valid in any well-generated reflection group…
Non-orientable branched coverings, -Hurwitz numbers, and positivity for multiparametric Jack expansions
Guillaume Chapuy, Maciej Dołęga
We introduce a one-parameter deformation of the 2-Toda tau-function of (weighted) Hurwitz numbers, obtained by deforming Schur functions into Jack symmetric functions. We show that…
On the number of coloured triangulations of -manifolds
Guillaume Chapuy, Guillem Perarnau
We give superexponential lower and upper bounds on the number of coloured -dimensional triangulations whose underlying space is an oriented manifold, when the number of simplice…
Local convergence and stability of tight bridge-addable graph classes
Guillaume Chapuy, Guillem Perarnau
A class of graphs is bridge-addable if given a graph in the class, any graph obtained by adding an edge between two connected components of is also in the class. The author…
Laplacian matrices and spanning trees of tree graphs
Philippe Biane, Guillaume Chapuy
If is a strongly connected finite directed graph, the set of rooted directed spanning trees of is naturally equipped with a structure of directed graph: ther…
Connectivity in bridge-addable graph classes: the McDiarmid-Steger-Welsh conjecture
Guillaume Chapuy, Guillem Perarnau
A class of graphs is bridge-addable if given a graph in the class, any graph obtained by adding an edge between two connected components of is also in the class. We prove a…
Generating functions of bipartite maps on orientable surfaces
Guillaume Chapuy, Wenjie Fang
We compute, for each genus , the generating function of (labelled) bipartite maps on the orientable surface of genus , with control on…
A bijection for rooted maps on general surfaces
Guillaume Chapuy, Maciej Dołęga
We extend the Marcus-Schaeffer bijection between orientable rooted bipartite quadrangulations (equivalently: rooted maps) and orientable labeled one-face maps to the case of all su…
The asymptotic number of -Avoiding Words with occurrences of each letter
Guillaume Chapuy
Following Ekhad and Zeilberger (The Personal Journal of Shalosh B. Ekhad and Doron Zeilberger, Dec 5 2014; see also arXiv:1412.2035), we study the asymptotics for large of the…
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…
Simple recurrence formulas to count maps on orientable surfaces
Sean R. Carrell, Guillaume Chapuy
We establish a simple recurrence formula for the number of rooted orientable maps counted by edges and genus. We also give a weighted variant for the generating polynomial…
Counting factorizations of Coxeter elements into products of reflections
Guillaume Chapuy, Christian Stump
In this paper, we count factorizations of Coxeter elements in well-generated complex reflection groups into products of reflections. We obtain a simple product formula for the expo…
The vertical profile of embedded trees
Mireille Bousquet-Mélou, Guillaume Chapuy
Consider a rooted binary tree with n nodes. Assign with the root the abscissa 0, and with the left (resp. right) child of a node of abscissa i the abscissa i-1 (resp. i+1). We prov…
A note on a Cayley graph of S_n
Guillaume Chapuy, Valentin Féray
Recently in graph theory several authors have studied the spectrum of the Cayley graph of the symmetric group S_n generated by the transpositions (1, i) for 2 <= i <= n. Several co…
The representation of the symmetric group on m-Tamari intervals
Mireille Bousquet-Mélou, Guillaume Chapuy, Louis-François Préville-Ratelle
An m-ballot path of size n is a path on the square grid consisting of north and east unit steps, starting at (0,0), ending at (mn,n), and never going below the line {x=my}. The set…
A simple model of trees for unicellular maps
Guillaume Chapuy, Valentin Féray, Eric Fusy
We consider unicellular maps, or polygon gluings, of fixed genus. A few years ago the first author gave a recursive bijection transforming unicellular maps into trees, explaining t…