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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).
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