J Austral Math Soc Ser A 43 pp375--384, 1987.

On a Conjecture of Carlitz

Wan Daqing

Abstract

A conjecture of Carlitz on permutation polynomials is as follows: Given an even positive integer n, there is a constant C_n, such that if F_q is a finite field of odd order q with q < C_n, then there are no permutation polynomials of degree n over F_q. The conjecture is a well-known problem in this area. It is easily proved of n is a power of 2. The only other cases in which solutions have been published are n = 6 (Dickson [5]) and n = 10 (Hayes [7]); see Lidl [11], Lausch and Nöbauer [9], and Lidl and Niederreiter [10] for remarks on this problem. In this paper, we prove that the Carlitz conjecture is true if n = 12 or n = 14, and give an equivalent version of the conjecture in terms of exceptional polynomials.

1980 AMS Subject Classification: 12C05

Browse the article

Authors

Wan Daqing

Department of Mathematics, The University of Washington, Seattle, Washington 98195, U.S.A.