Algebraic Structure of Permutational Polynomials over ${\mathbb{F}}_{q^n}$

In this paper, we propose a new algebraic structure of permutation polynomials over ${\mathbb{F}}_{q^n}$. As an application of this new algebraic structure, we give some classes of new PPs over ${\mathbb{F}}_{q^n}$ and answer an open problem in Charpin and Kyureghyan.