{"title":"Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form","authors":"Alexander Bors, Qiang Wang","doi":"10.4208/cmr.2021-0029","DOIUrl":null,"url":null,"abstract":"This paper is concerned with so-called index d generalized cyclotomic mappings of a finite field Fq, which are functions Fq → Fq that agree with a suitable monomial function x 7→ axr on each coset of the index d subgroup of Fq. 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 Fq and pertain to cycle structures, the classification of (q − 1)-cycles and involutions, as well as inversion.","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究通讯","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4208/cmr.2021-0029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
This paper is concerned with so-called index d generalized cyclotomic mappings of a finite field Fq, which are functions Fq → Fq that agree with a suitable monomial function x 7→ axr on each coset of the index d subgroup of Fq. 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 Fq and pertain to cycle structures, the classification of (q − 1)-cycles and involutions, as well as inversion.