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arXiv · 2307.02366

Modular binomials with an application to periodic sequences

Luisa Fiorot·Riccardo Gilblas·Alberto Tonolo
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Abstract

We study, through new recurrence relations for certain binomial coefficients modulo a power of a prime, the evolution of the primitives of a modular periodic sequence. We prove that we can reduce to study primitives of constant sequences and that the latter are controlled by modular binomial coefficients. Finally we apply our results to describe the dynamics of the primitives of the sequence considered by the Romanian composer Vieru in his "Book of Modes".

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Luisa Fiorot, Riccardo Gilblas, Alberto Tonolo. 2023-07-05. Modular binomials with an application to periodic sequences. https://arxiv.org/abs/2307.02366

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