On permutation polynomials over finite fields. (1987) - Mollin, R. A.; Small, C.
Abstract : A polynomialf over a finite fieldF is called a permutation polynomial if the mappingF → F defined byf is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integerm, the cardinality of finite fields admitting permutation polynomials of degreem is bounded.