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WALKS IN THE QUARTER PLANE: GENUS ZERO CASE

Abstract : 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.
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Submitted on : Thursday, November 5, 2020 - 5:45:52 PM
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Thomas Dreyfus, Charlotte Hardouin, Julien Roques, Michael Singer. WALKS IN THE QUARTER PLANE: GENUS ZERO CASE. Journal of Combinatorial Theory, Series A, Elsevier, 2020, 174, pp.105251. ⟨10.1016/j.jcta.2020.105251⟩. ⟨hal-02990927⟩

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