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math.CO2026
Walks in the quadrant with interacting boundaries : genus zero case
Pierre Bonnet
The study of lattice walks restricted to the first quadrant has shed a lot of interest in the past twenty years. In particular, there has been an important effort to classify model…
math.CO2025
A Galois structure on the orbit of large steps walks in the quadrant
Pierre Bonnet, Charlotte Hardouin
The enumeration of weighted walks in the quarter plane reduces to studying a functional equation with two catalytic variables. When the steps of the walk are small, Bousquet-Mélou…
math.CO2024
Galoisian structure of large steps walks in the quadrant
Pierre Bonnet, Charlotte Hardouin
The enumeration of walks in the quarter plane confined in the first quadrant has attracted a lot of attention over the past fifteenth years. The generating functions associated to…