Anbar, Nurdagül and Odžak, Almasa and Patel, Vandita and Quoos, Luciane and Somoza, Anna and Topuzoğlu, Alev
(2018)
*On the Carlitz rank of permutation polynomials over finite fields: recent developments.*
In: Bouw, Irene I. and Ozman, Ekin and Johnson-Leung, Jennifer and Newton, Rachel, (eds.)
Women in Numbers Europe II: Contributions to Number Theory and Arithmetic Geometry.
Association for Women in Mathematics Series, 11.
Springer Cham, pp. 39-55.
ISBN 978-3-319-74997-6 (Print) 978-3-319-74998-3 (Online)

Official URL: https://dx.doi.org/10.1007/978-3-319-74998-3_4

## Abstract

The Carlitz rank of a permutation polynomial over a finite field Fq is a simple concept that was introduced in the last decade. In this survey article, we present various interesting results obtained by the use of this notion in the last few years. We emphasize the recent work of the authors on the permutation behavior of polynomials f + g, where f is a permutation over Fq of a given Carlitz rank, and g∈Fq[x] is of prescribed degree. The relation of this problem to the well-known Chowla–Zassenhaus conjecture is described. We also present some initial observations on the iterations of a permutation polynomial f∈Fq[x] and hence on the order of f as an element of the symmetric group S q .

Item Type: | Book Section / Chapter |
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Uncontrolled Keywords: | Carlitz rank; Finite fields; Permutation polynomials |

Divisions: | Faculty of Engineering and Natural Sciences |

Depositing User: | Alev Topuzoğlu |

Date Deposited: | 31 Jul 2023 16:08 |

Last Modified: | 31 Jul 2023 16:08 |

URI: | https://research.sabanciuniv.edu/id/eprint/46649 |