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. doi:10.7907/24QB-M779. https://resolver.caltech.edu/CaltechETD:etd-06022006-085847

Abstract

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 1_S•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.

Thesis Files