42 citations · 260 across the 31 of their papers we have counts for
7 papers · 1 filter
Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness
Thomas Dreyfus, Andrew Elvey Price, Kilian Raschel
In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in…
Differential algebraic generating series of weighted walks in the quarter plane
Thomas Dreyfus
In the present paper we study the nature of the trivariate generating series of weighted walks in the quarter plane. Combining the results of this paper to previous ones, we comple…
On the nature of four models of symmetric walks avoiding a quadrant
Thomas Dreyfus, Amélie Trotignon
We study the nature of the generating series of some models of walks with small steps in the three quarter plane. More precisely, we restrict ourselves to the situation where the g…
On the Kernel curves associated with walks in the quarter plane
Thomas Dreyfus, Charlotte Hardouin, Julien Roques +1
The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel poly…
Length derivative of the generating series of walks confined in the quarter plane
Thomas Dreyfus, Charlotte Hardouin
In the present paper, we use difference Galois theory to study the nature of the generating function counting walks with small steps in the quarter plane. These series are trivaria…
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 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.…