Permutations from an arithmetic setting

Autor(es)

Reis, Lucas ^[1] ; Ribas, Savio ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Fed Ouro Preto, Inst Ciencias Exatas & Biol, Dept Matemat, BR-35400000 Ouro Preto, MG - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE MATHEMATICS; v. 343, n. 8 AUG 2020.
• Citações Web of Science: 0

Resumo

Let m, n be positive integers such that m > 1 divides n. In this paper, we introduce a special class of piecewise-affine permutations of the finite set {[}1, n] := [1, ..., n] with the property that the reduction (mod m) of m consecutive elements in any of its cycles is, up to a cyclic shift, a fixed permutation of {[}1, m]. Our main result provides the cycle decomposition of such permutations. We further show that such permutations give rise to permutations of finite fields. In particular, we explicitly obtain classes of permutation polynomials of finite fields whose cycle decomposition and its inverse are explicitly given. (C) 2020 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 18/03038-2 - Mapas polinomiais em corpos finitos e suas aplicações
• Beneficiário: Lucas da Silva Reis
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado