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

2022/11/14 by Notarantonio, Hadrien, Yurkevich, Sergey
#Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.07298

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).

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