# Accession Number:

## ADA009813

# Title:

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

# Descriptive Note:

# Corporate Author:

## CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES

# Personal Author(s):

# Report Date:

## 1974-08-30

# Pagination or Media Count:

## 17.0

# Abstract:

Let F denote a finite field and let f sub n x n denote the n x n matrices over F. A function fF 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 fx an element of Fin bracketsx 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.

# Descriptors:

# Subject Categories:

- Air Breathing Engines (Unconventional)