Permutation polynomials from piecewise functions

Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we present some classes of explicit permutation polynomials of the forms similar to (xpk+ax+δ)pn−1d+1−ax, d=2,3,4,6d=2,3,4,6. The results here generalize the similar results obtained in [5] and [15] greatly.