We describe the equivalence classes of permutations of  F_q  induced by binomials, modulo the equivalence of composition on both sides with permutations induced by monomials. This enables us to count the number of permutations of  F_q  induced by binomials. This generalizes a result of Masuda, Panario and Wang, which treats the special case that  q  is prime and either  (q-1) / 2  or  (q-1) / 4  is prime.

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