A Theory of Permutation Polynomials Using Compositional Attractors

Author: Ashlock, Daniel Abram

Year: 1990

Degree: Dissertation (Ph.D.)

Advisors: Wales, David B.; Wilson, Richard M.

Committee Members: Wilson, Richard M.; Aschbacher, Michael; Ramakrishnan, Dinakar; Wales, David B.; Luxemburg, W. A. J.

Option: Mathematics

DOI: 10.7907/24QB-M779

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 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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