Michael E. Zieve

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Ritt studied the functional decomposition of a univariate complex polynomial f into prime (indecomposable) polynomials, f = u1 ◦ u2 ◦ · · · ◦ ur. His main achievement was a procedure for obtaining any decomposition of f from any other by repeatedly applying certain transformations. However, Ritt’s results provide no control on the number of times one must(More)
In the 1920’s, Ritt studied the operation of functional composition g ◦ h(x) = g(h(x)) on complex rational functions. In the case of polynomials, he described all the ways in which a polynomial can have multiple ‘prime factorizations’ with respect to this operation. Despite significant effort by Ritt and others, little progress has been made towards solving(More)
We present a general technique for obtaining permutation polynomials over a finite field from permutations of a subfield. By applying this technique to the simplest classes of permutation polynomials on the subfield, we obtain several new families of permutation polynomials. Some of these have the additional property that both f(x) and f(x) + x induce(More)