By elementary theory of groups one can verify that the set of permutation polynomial vectors over the residue class ring Z/p~nZ is a group according to composite of mappings,hence the inverse of each permutation polynomial vector over Z/p~nZ is also a permutation polynomial vector.

Permutation polynomials play an important role in communication field.

Dickson polynomials are of special source of permutation polynomials over finite fields.

With some results of polynomial theory in finite field, a criterion theorem for a permutation polynomial to be an orthormorphic permutation polynomial is presented.

By analytic viewpoint, the author gives a proof of the result that the inverse of any permutation polynomial over Z/pnZ can be represented by a polynomial and so all permutation polynomials over Z/pnZ form a group according to the operation of composite of maps and reduction mod J.

The author studies a class of singular permutation polynomials in n(n≥3) indeterminates modulo p, gives a sufficient condition for them to be permutation polynomials modulo p l(l>1).

In this paper we prove Nikolskii inequality of vector polynomial with norm B(p,q) for Erds weights.

In this paper,we discussthe problem that vector polynomial approximation f(t).

Nonexistence of a special kind of orthomorphic permutation polynomials over finite fields with characteristic 2;

The concept of orthomorphic permutation polynomial is given and several properties about it are proved, on the basis of which we give characterization for orthomorphic permutations.

In this paper,the author give the spectra characterizations of nonsigular feedback polynomials and local permutation polynomials over finite fields and residue class rings,and simplify existing results over prime fields,and provide a new proof method for the spectra characterization of correlation immune functions over finite fields and residue class rings.