42 citations · 260 across the 31 of their papers we have counts for
3 papers · 1 filter
Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks
Thomas Dreyfus, Kilian Raschel
We consider weighted small step walks in the positive quadrant, and provide algebraicity and differential transcendence results for the underlying generating functions: we prove th…
On the multiple-scale analysis for some linear partial -difference and differential equations with holomorphic coefficients
Thomas Dreyfus, Alberto Lastra, Stéphane Malek
The analytic and formal solutions of certain family of -difference-differential equations under the action of a complex perturbation parameter is considered. The previous study…
On the nature of the generating series of walks in the quarter plane
Thomas Dreyfus, Charlotte Hardouin, Julien Roques +1
In the present paper, we introduce a new approach, relying on the Galois theory of difference equations, to study the nature of the generating series of walks in the quarter plane.…