TY - JOUR
T1 - Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form
AU - Bors , Alexander
AU - Wang , Qiang
JO - Communications in Mathematical Research 
VL - 2
SP - 246
EP - 318
PY - 2022
DA - 2022/02
SN - 38
DO - http://doi.org/10.4208/cmr.2021-0029
UR - https://global-sci.org/intro/article_detail/cmr/20273.html
KW - Finite fields, cyclotomy, cyclotomic mappings, permutation polynomials, wreath product, cycle structure, involution.
AB - <p style="text-align: justify;">This paper is concerned with so-called index $d$ generalized cyclotomic mappings of a finite field $\mathbb{F}_q$, which are functions $\mathbb{F}_q \rightarrow \mathbb{F}_q$&nbsp;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 <span style="text-align: justify;">$\mathbb{F}_q$</span> and pertain to cycle structures,
the classification of $(q−1)$-cycles and involutions, as well as inversion.</p>