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

2020/12/01 by Alin Bostan, Manuel Kauers, Bostan, Alin +3 · 1 citation
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Polynomial and algebraic computation #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2012.00816

openalex publication_date 2020/12/01 · openalex created_date 2020/12/07 · openalex updated_date 2026/07/28

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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