On the Carlitz rank of permutation polynomials

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• 作者：Esen Aksoy ; Ayç ; a Ç ; eş ; melioğ ; lu ; Wilfried Meidl ; Alev Topuzoğ ; lu
• 关键词：Permutation polynomials of finite fields ; Carlitz rank ; Enumeration of permutation polynomials ; Stirling numbers of the first kind
• 刊名：Finite Fields and Their Applications
• 出版年：2009
• 出版时间：August 2009
• 年：2009
• 卷：15
• 期：4
• 页码：428-440
• 全文大小：229 K

文摘

A well-known result of Carlitz, that any permutation polynomial (x) of a finite field is a composition of linear polynomials and the monomial x^q−2, implies that (x) can be represented by a polynomial , for some n0. The smallest integer n, such that represents (x) is of interest since it is the least number of “inversions” x^q−2, needed to obtain (x). We define the Carlitz rank of (x) as n, and focus here on the problem of evaluating it. We also obtain results on the enumeration of permutations of with a fixed Carlitz rank.