@Article{CMR-38-246,
author = {Bors , Alexander and Wang , Qiang},
title = {Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form},
journal = {Communications in Mathematical Research },
year = {2022},
volume = {38},
number = {2},
pages = {246--318},
abstract = {<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>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2021-0029},
url = {http://global-sci.org/intro/article_detail/cmr/20273.html}
}