A Caltech Library Service

A Theory of Permutation Polynomials Using Compositional Attractors


Ashlock, Daniel Abram (1990) A Theory of Permutation Polynomials Using Compositional Attractors. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/24QB-M779.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Wales, David B. (advisor)
  • Wilson, Richard M. (co-advisor)
Thesis Committee:
  • Wilson, Richard M. (chair)
  • Aschbacher, Michael
  • Ramakrishnan, Dinakar
  • Wales, David B.
  • Luxemburg, W. A. J.
Defense Date:7 May 1990
Non-Caltech Author Email:dashlock (AT)
Record Number:CaltechETD:etd-06022006-085847
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2397
Deposited By: Imported from ETD-db
Deposited On:02 Jun 2006
Last Modified:14 Jan 2022 01:13

Thesis Files

PDF (Ashlock_da_1990.pdf) - Final Version
See Usage Policy.


Repository Staff Only: item control page