## Quasi-permutation polynomials.(English)Zbl 1224.11096

Summary: A quasi-permutation polynomial is a polynomial which is a bijection from one subset of a finite field onto another with the same number of elements. This is a natural generalization of the familiar permutation polynomials. Basic properties of quasi-permutation polynomials are derived. General criteria for a quasi-permutation polynomial extending the well-known Hermite’s criterion for permutation polynomials as well as a number of other criteria depending on the permuted domain and range are established. Different types of quasi-permutation polynomials and the problem of counting quasi-permutation polynomials of fixed degree are investigated.

### MSC:

 11T06 Polynomials over finite fields

### Keywords:

finite field; permutation polynomial
Full Text:

### References:

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