This is a synopsis of the current state of knowledge about exceptional polynomials over finite fields, namely, polynomials in F_q[x]  which induce bijections on F_qⁿ  for infinitely many n. These polynomials have applications to various areas of pure and applied math. One novel aspect of this synopsis is the new connection between low-degree permutation polynomials and exceptional rational functions over difference fields in Remark 8.4.24.

Michael Zieve:  home page   publication list