{"title":"广义环形映射:多项式、环形和环积形式之间的切换","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":"{\"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}","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}
Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form
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.