Geodesic
Polynomial Automorphisms Over Finite Fields
Serdica Mathematical Journal, Tome 27 (2001) no. 4, pp. 343-350.

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It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).
Keywords: Polynomial Automorphisms, Tame Automorphisms, Affine Spaces Over Finite Fields, Primitive Groups 
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     author = {Maubach, Stefan},
     title = {Polynomial {Automorphisms} {Over} {Finite} {Fields}},
     journal = {Serdica Mathematical Journal},
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     number = {4},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2001_27_4_a5/}
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Maubach, Stefan. Polynomial Automorphisms Over Finite Fields. Serdica Mathematical Journal, Tome 27 (2001) no. 4, pp. 343-350. http://geodesic.mathdoc.fr/item/SMJ2_2001_27_4_a5/