Also, these look promising: When Does a Polynomial Over a Finite Field Permute the Elements of the Field? Rudolf Lidl, Gary L. Mullen The American Mathematical Monthly Vol. 95, No. 3 (Mar., 1988), pp. 243-246 When Does a Polynomial over a Finite Field Permute the Elements of the Field?, II Rudolf Lidl and Gary L. Mullen The American Mathematical Monthly Vol. 100, No. 1 (Jan., 1993), pp. 71-74 —Dan
On Mar 20, 2016, at 10:14 AM, Victor Miller <victorsmiller@gmail.com> wrote:
More general are "exceptional polynomials" which were the subject of Dickson's thesis. A polynomial over a finite field is exceptional if it induces a one-to-one mapping on infinitely many extensions of the finite field. The following recent paper talks about classes of exceptional polynomials in characteristic 2: http://annals.math.princeton.edu/wp-content/uploads/annals-v172-n2-p12-p.pdf