Work

Periodic sequences, binomials modulo a prime power, and a math/music application

Year: 2024

Type: article

Abstract: We study, through new recurrence relations for certain binomial coefficients modulo a power of a prime, the evolution of the iterated anti-differences of periodic sequences modulo m . We prove that one can reduce to study iterated anti-differences of constant sequences. Finally we apply our results to describe the dynamics of the iterated applications of the Vieru operator to the sequence considered by the Romanian composer Vieru in his Book of Modes [20] .

Source: Advances in Applied Mathematics

DOI: 10.1016/j.aam.2024.102786

Authors: Luisa Fiorot, Riccardo Gilblas, Alberto Tonolo

Institution: University of Padua

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,000

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni, NextGenerationEU