Séminaire Lotharingien de Combinatoire, 89B.13 (2023), 12 pp.
Hadrien Notarantonio and Sergey Yurkevich
Effective Algebraicity for Solutions of Systems of Functional Equations with one Catalytic Variable
Abstract.
We study systems of n ≥ 1 discrete differential equations of order k ≥ 1 in one catalytic variable and provide a constructive and elementary proof of algebraicity of their solutions. This yields effective bounds and a systematic method for computing the minimal polynomials. Our approach is a generalization of the pioneering work by Bousquet-Mélou and Jehanne (2006).
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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