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Title: Permutations from an arithmetic setting.
Authors: Reis, Lucas
Ribas, Sávio
Keywords: Cycle decomposition
m-th residues
Finite fields
Issue Date: 2020
Citation: REIS, L.; RIBAS, S. Permutations from an arithmetic setting. Discrete Mathematics, v. 343, n. 8, artigo 111923, 2020. Disponível em: <>. Acesso em: 06 jul. 2022.
Abstract: 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.
ISSN: 0012-365X
Appears in Collections:DEMAT - Artigos publicados em periódicos

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