Thomas Dreyfus, Charlotte Hardouin, Julien Roques, Michael F. Singer
Published 2017-10-08Version 1
In the present paper, we use Galois theory of difference equations to study the nature of the generating series of (weighted) walks in the quarter plane with genus zero kernel. Using this approach, we are able to prove that the generating series do not satisfy any nontrivial nonlinear algebraic differential equation with rational coefficients.
Length derivative of the generating series of walks confined in the quarter plane
On the nature of the generating series of walks in the quarter plane
Polyharmonic Functions in the Quarter Plane
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