Date of Award
Spring 5-9-2015
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
Dr. Florian Enescu
Abstract
Polynomial functions over finite fields are a major tool in computer science and electrical engineering and have a long history. Some of its aspects, like interpolation and permutation polynomials are described in this thesis. A complete characterization of subfield compatible polynomials (f in E[x] such that f(K) is a subset of L, where K,L are subfields of E) was recently given by J. Hull. In his work, he introduced the Frobenius permutation which played an important role. In this thesis, we fully describe the cycle structure of the Frobenius permutation. We generalize it to a permutation called a monomial permutation and describe its cycle factorization. We also derive some important congruences from number theory as corollaries to our work.
DOI
https://doi.org/10.57709/7028553
Recommended Citation
Virani, Adil B., "Frobenius-Like Permutations and Their Cycle Structure." Thesis, Georgia State University, 2015.
doi: https://doi.org/10.57709/7028553