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Conference Papers Year : 2023

Effective algebraicity for solutions of systems of functional equations with one catalytic variable

Abstract

We study systems of $n \geq 1$ discrete differential equations of order $k\geq1$ 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).

Dates and versions

hal-03854264 , version 1 (15-11-2022)

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Hadrien Notarantonio, Sergey Yurkevich. Effective algebraicity for solutions of systems of functional equations with one catalytic variable. 35th international conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2023), Jul 2023, Davis, CA, United States. ⟨hal-03854264⟩
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