A theory of permutation polynomials using compositional attractors

Citation

Ashlock, Daniel Abram (1990) A theory of permutation polynomials using compositional attractors. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-06022006-085847

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In this work I will develop a theory of permutation polynomials with coefficients over finite commutative rings. The general situation will be that we have a finite ring R and a ring S, both with 1, with S commutative, and with a scalar multiplication of elements of R by elements of S, so that for each r in R 1s • r = r and with the scalar multiplication being R bilinear. When all these conditions hold, I will call R an S-algebra. A permutation polynomial will be a polynomial of S[x] with the property that the function r [...] f(r) is a bijection, or permutation, of R.

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