21 citations · 60 across the 11 of their papers we have counts for
15 papers
Cayley trees and increasing 1,2-trees: let's twist!
Julien Courtiel, Matthieu Dien, Paul Dorbec
An increasing 1,2-tree is a labeled graph formed by starting with a vertex and then repeatedly attaching a leaf to a vertex or a triangle to an edge, the labeling of the vertices c…
Theoretical analysis of git bisect
Julien Courtiel, Paul Dorbec, Romain Lecoq
In this paper, we consider the problem of finding a regression in a version control system (VCS), such as git. The set of versions is modelled by a Directed Acyclic Graph (DAG) whe…
Orientable Burning Number of Graphs
Julien Courtiel, Paul Dorbec, Tatsuya Gima +2
In this paper, we introduce the problem of finding an orientation of a given undirected graph that maximizes the burning number of the resulting directed graph. We show that the pr…
Bijections between walks inside a triangular domain and Motzkin paths of bounded amplitude
Julien Courtiel, Andrew Elvey Price, Irène Marcovici
This paper solves an open question of Mortimer and Prellberg asking for an explicit bijection between two families of walks. The first family is formed by what we name triangular w…
Next-to leading log expansions by chord diagrams
Julien Courtiel, Karen Yeats
Green functions in a quantum field theory can be expanded as bivariate series in the coupling and a scale parameter. The leading logs are given by the main diagonal of this expansi…
Asymptotic Distribution of Parameters in Random Maps
Olivier Bodini, Julien Courtiel, Sergey Dovgal +1
We consider random rooted maps without regard to their genus, with fixed large number of edges, and address the problem of limiting distributions for six different parameters: vert…
Connected chord diagrams and bridgeless maps
Julien Courtiel, Karen Yeats, Noam Zeilberger
We present a surprisingly new connection between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorial maps on th…
Bijections for Weyl Chamber walks ending on an axis, using arc diagrams and Schnyder woods
Julien Courtiel, Éric Fusy, Mathias Lepoutre +1
In the study of lattice walks there are several examples of enumerative equivalences which amount to a trade-off between domain and endpoint constraints. We present a family of suc…
Weighted Lattice Walks and Universality Classes
Julien Courtiel, Stephen Melczer, Marni Mishna +1
In this work we consider two different aspects of weighted walks in cones. To begin we examine a particular weighted model, known as the Gouyou-Beauchamps model. Using the theory o…
Terminal chords in connected chord diagrams
Julien Courtiel, Karen Yeats
Rooted connected chord diagrams form a nice class of combinatorial objects. Recently they were shown to index solutions to certain Dyson-Schwinger equations in quantum field theory…
Tableau sequences, open diagrams, and Baxter families
Sophie Burrill, Julien Courtiel, Eric Fusy +2
Walks on Young's lattice of integer partitions encode many objects of algebraic and combinatorial interest. Chen et al. established connections between such walks and arc diagrams.…
Counting, generating and sampling tree alignments
Cedric Chauve, Julien Courtiel, Yann Ponty
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is a…
A general notion of activity for the Tutte polynomial
Julien Courtiel
In the literature can be found several descriptions of the Tutte polynomial of graphs. Tutte defined it thanks to a notion of activity based on an ordering of the edges. Thereafter…
Spanning forests in regular planar maps
Mireille Bousquet-Mélou, Julien Courtiel
We address the enumeration of p-valent planar maps equipped with a spanning forest, with a weight z per face and a weight u per connected component of the forest. Equivalently, we…
Gerechte Designs with Rectangular Regions
J. Courtiel, E. R. Vaughan
A \emph{gerechte framework} is a partition of an array into regions of cells each. A \emph{realization} of a gerechte framework is a latin square of order …