(untitled) (Communications in Mathematical Research, 2022)
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 xax^r 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.