The Number of Polynomial Functions Which Permute the Matrices over a Finite Field,

Abstract

Let F denote a finite field and let f sub (n x n) denote the n x n matrices over F. A function f:F sub (n x n) maps to F sub (n x n) is called a (scalar) polynomial function on F sub (n x n) if and only if there exists a polynomial f(x) an element of F(in brackets:(x)) which represents f under substitution. A formula is obtained for the number of polynomial function on F sub (n x n) which are permutations of F sub (n x n). In the process a procedure is outlined for obtaining a unique polynomial representations of each permutation polynomial function on F sub (n x n).

Document Details

Document Type
Technical Report
Publication Date
Aug 30, 1974
Accession Number
ADA009813

Entities

People

  • Joel V. Brawley Jr.

Organizations

  • Clemson University

Tags

DTIC Thesaurus Topics

  • Permutations
  • Polynomials

Fields of Study

  • Mathematics

Readers

  • Linear Algebra