Aksoy, Esen and Çeşmelioğlu, Ayça and Meidl, Wilfried and Topuzoğlu, Alev (2009) On the Carlitz rank of permutation polynomials. Finite Fields and Their Applications, 15 (4). pp. 428440. ISSN 10715797
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Official URL: http://dx.doi.org/10.1016/j.ffa.2009.02.006
Abstract
A wellknown result of Carlitz, that any permutation polynomial p(x) of a finite field Fq is a composition of linear polynomials and the monomial x(q2). implies that V(x) can be represented by a polynomial Pn(x) = (...((a(0)x + a(1))(q2) + a(2))(q2)...+ a(n))(q2) + a(n+1). for some n >= 0. The smallest integer n, such that P,,(x) represents p(x) is of interest since it is the least number of "inversions" x(q2), needed to obtain p(x). We define the Carlitzrank of p(x) as n, and focus here on the problem of evaluating it. We also obtain results on the enumeration of permutations of Fq with a fixed Carlitz rank.
Item Type:  Article 

Uncontrolled Keywords:  Permutation polynomials of finite fields; Carlitz rank; Enumeration of permutation polynomials; Stirling numbers of the first kind 
Subjects:  Q Science > QA Mathematics > QA150272.5 Algebra 
Divisions:  Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics 
Depositing User:  Alev Topuzoğlu 
Date Deposited:  03 Dec 2009 16:48 
Last Modified:  24 Jul 2019 11:09 
URI:  https://research.sabanciuniv.edu/id/eprint/13230 
Available Versions of this Item

On the Carlitz rank of permutation polynomials. (deposited 27 May 2009 11:45)
 On the Carlitz rank of permutation polynomials. (deposited 03 Dec 2009 16:48) [Currently Displayed]