full
search.png

Search

close.png

Cancel

arrow
Volume 38, Issue 2
Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form

Alexander Bors & Qiang Wang

DOI: 10.4208/cmr.2021-0029

Commun. Math. Res., 38 (2022), pp. 246-318.

Published online: 2022-02

Preview Purchase PDF 2431 36205

Cited by

google scholar semantic scholar
Export citation
  • Abstract

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 $\mathbb{F}^∗_q$. 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.

  • Keywords

Finite fields, cyclotomy, cyclotomic mappings, permutation polynomials, wreath product, cycle structure, involution.

  • AMS Subject Headings

Primary: 11T22. Secondary: 11A07, 11T06, 20E22

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CMR-38-246, author = {Bors , Alexander and Wang , Qiang}, title = {Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form}, journal = {Communications in Mathematical Research }, year = {2022}, volume = {38}, number = {2}, pages = {246--318}, abstract = {

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 $\mathbb{F}^∗_q$. 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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0029}, url = {http://global-sci.org/intro/article_detail/cmr/20273.html} }
TY - JOUR T1 - Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form AU - Bors , Alexander AU - Wang , Qiang JO - Communications in Mathematical Research VL - 2 SP - 246 EP - 318 PY - 2022 DA - 2022/02 SN - 38 DO - http://doi.org/10.4208/cmr.2021-0029 UR - https://global-sci.org/intro/article_detail/cmr/20273.html KW - Finite fields, cyclotomy, cyclotomic mappings, permutation polynomials, wreath product, cycle structure, involution. AB -

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 $\mathbb{F}^∗_q$. 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.

Bors , Alexander and Wang , Qiang. (2022). Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form. Communications in Mathematical Research . 38 (2). 246-318. doi:10.4208/cmr.2021-0029
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard