Modular binomials with an application to periodic sequences
Number Theory
2023-07-06 v1 Combinatorics
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".
Cite
@article{arxiv.2307.02366,
title = {Modular binomials with an application to periodic sequences},
author = {Luisa Fiorot and Riccardo Gilblas and Alberto Tonolo},
journal= {arXiv preprint arXiv:2307.02366},
year = {2023}
}