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

作　　者：Alexander Bors Qiang Wang 

机构地区：[1]School of Mathematics and Statistics,Carleton University,1125 Colonel By Drive,Ottawa ON K1S 5B6,Canada

出　　处：《Communications in Mathematical Research》2022年第2期246-318,共73页数学研究通讯（英文版）

摘　　要：This paper is concerned with so-called index d generalized cyclotomic mappings of a finite field F_(q), which are functions F_(q)→F_(q) that agree with a suitable monomial function x↦axr on each coset of the index d subgroup of 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 F_(q) and pertain to cycle structures, the classification of (q−1)-cycles and involutions, as well as inversion.

关 键 词：Finite fields CYCLOTOMY cyclotomic mappings permutation polynomials wreath product cycle structure INVOLUTION 

分 类 号：O17[理学—数学]