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The generating function of Kreweras walks with interacting boundaries is not algebraic

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Abstract

Beaton, Owczarek and Xu (2019) studied generating functions of Kreweras walks and of reverse Kreweras walks in the quarter plane, with interacting boundaries. They proved that for the reverse Kreweras step set, the generating function is always algebraic, and for the Kreweras step set, the generating function is always D-finite. However, apart from the particular case where the interactions are symmetric in $x$ and $y$, they left open the question of whether the latter one is algebraic. Using computer algebra tools, we confirm their intuition that the generating function of Kreweras walks is not algebraic, apart from the particular case already identified.
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hal-03084659 , version 1 (21-12-2020)

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Alin Bostan, Manuel Kauers, Thibaut Verron. The generating function of Kreweras walks with interacting boundaries is not algebraic. FPSAC'21 - Formal power series and algebraic combinatorics, Jul 2021, Ramat Gan, Israel. pp.12. ⟨hal-03084659⟩
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