The Number of Polynomial Functions Which Permute the Matrices over a Finite Field,
CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES
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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.
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