In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map is a bijection. In case the ring is a finite field, the Dickson polynomials, which are closely related to the Chebyshev polynomials, provide examples. There are some situations in which these are essentially the only permutation polynomials over finite fields.
In the case of finite rings Z/nZ, such polynomials have also been studied and applied in the interleaver component of error detection and correction algorithms.
Read more about Permutation Polynomial: Quadratic Permutation Polynomials (QPP), Higher Degree Polynomials, Finite Fields, Geometric Examples, Schur's Conjecture