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.
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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.