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

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Wreath product Cyclotomic polynomial Mathematics Product (mathematics) Polynomial Reciprocal polynomial Pure mathematics Combinatorics Algebra over a field Discrete mathematics Matrix polynomial Mathematical analysis Geometry

Alexander Bors , Qiang Wang Qiang Wang ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.4208/cmr.2021-0029 · OA: W3134795428

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 $\mathbb{F}_q^{\ast}$. 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.