WALKS IN THE QUARTER PLANE: GENUS ZERO CASE

Thomas Dreyfus (1) , Charlotte Hardouin (2) , Julien Roques (3) , Michael F. Singer

1 IRMA - Institut de Recherche Mathématique Avancée
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 ICJ - Institut Camille Jordan

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 curve. Using this approach, we prove that the generating series do not satisfy any nontrivial (possibly nonlinear) algebraic differential equation with rational coefficients.

Domaines: Mathématiques [math]

Thomas Dreyfus, Charlotte Hardouin, Julien Roques, Michael F. Singer. WALKS IN THE QUARTER PLANE: GENUS ZERO CASE. Journal of Combinatorial Theory, Series A, 2020, 174, pp.105251. ⟨10.1016/j.jcta.2020.105251⟩. ⟨hal-02990927⟩