183 citations · 362 across the 15 of their papers we have counts for
16 papers
Enumeration of three-quadrant walks via invariants: some diagonally symmetric models
Mireille Bousquet-Mélou
In the past 20 years, the enumeration of plane lattice walks confined to a convex cone -- normalized into the first quadrant -- has received a lot of attention, stimulated the deve…
Walks avoiding a quadrant and the reflection principle
Mireille Bousquet-Mélou, Michael Wallner
We continue the enumeration of plane lattice walks with small steps avoiding the negative quadrant, initiated by the first author in 2016. We solve in detail a new case, namely the…
Plane bipolar orientations and quadrant walks
Mireille Bousquet-Mélou, Éric Fusy, Kilian Raschel
Bipolar orientations of planar maps have recently attracted some interest in combinatorics, probability theory and theoretical physics. Plane bipolar orientations with edges ar…
Eulerian orientations and the six-vertex model on planar map
Mireille Bousquet-Mélou, Andrew Elvey Price, Paul Zinn-Justin
We address the enumeration of planar 4-valent maps equipped with an Eulerian orientation by two different methods, and compare the solutions we thus obtain. With the first method w…
Counting walks with large steps in an orthant
Alin Bostan, Mireille Bousquet-Mélou, Stephen Melczer
In the past fifteen years, the enumeration of lattice walks with steps takenin a prescribed set S and confined to a given cone, especially the firstquadrant of the plane, has been…
The generating function of planar Eulerian orientations
Mireille Bousquet-Mélou, Andrew Elvey Price
The enumeration of planar maps equipped with an Eulerian orientation has attracted attention in both combinatorics and theoretical physics since at least 2000. The case of 4-valent…