Geodesic
Quasi-permutation polynomials
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 457-488.

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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.
Classification : 11T55, 12E05, 12Y05
Keywords: finite fields; permutation polynomials 
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     title = {Quasi-permutation polynomials},
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     zbl = {1224.11096},
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Laohakosol, Vichian; Janphaisaeng, Suphawan. Quasi-permutation polynomials. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 457-488. http://geodesic.mathdoc.fr/item/CMJ_2010__60_2_a12/