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-M\'elou and Jehanne (2006).
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