Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form

Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form

Year:    2022

Author:    Alexander Bors, Qiang Wang

Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 246–318

Abstract

This paper is concerned with so-called index $d$ generalized cyclotomic mappings of a finite field $\mathbb{F}_q$, which are functions $\mathbb{F}_q \rightarrow \mathbb{F}_q$ that agree with a suitable monomial function $x\mapsto ax^r$ on each coset of the index $d$ subgroup of $\mathbb{F}^∗_q$. We discuss two important rewriting procedures in the context of generalized cyclotomic mappings and present applications thereof that concern index $d$ generalized cyclotomic permutations of $\mathbb{F}_q$ and pertain to cycle structures, the classification of $(q−1)$-cycles and involutions, as well as inversion.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cmr.2021-0029

Communications in Mathematical Research , Vol. 38 (2022), Iss. 2 : pp. 246–318

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    73

Keywords:    Finite fields cyclotomy cyclotomic mappings permutation polynomials wreath product cycle structure involution.

Author Details

Alexander Bors

Qiang Wang

  1. A survey of compositional inverses of permutation polynomials over finite fields

    Wang, Qiang

    (2024)

    https://doi.org/10.1007/s10623-024-01436-4 [Citations: 0]