Permutation Polynomials: A Matrix Analogue of Schur's Conjecture and a Survey of Recent Results

Authors:
G. L. Mullen
Affiliations:
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Venue:
Finite Fields and Their Applications
Year:
1995

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Abstract

We consider a matrix analogue of Schur's conjecture concerning permutation polynomials induced by polynomials with integral coefficients. For any fixed integer m = 1 we consider polynomials with integral coefficients which induce permutations on the ring of all m x m matrices over the finite field F"p for infinitely many primes p. We also provide a survey of recent results concerning permutation polynomials over finite fields.