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

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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 × m matrices over the finite field Fp for infinitely many primes p. We also provide a survey of recent results concerning permutation polynomials over finite fields.

Original languageEnglish (US)
Pages (from-to)242-258
Number of pages17
JournalFinite Fields and their Applications
Volume1
Issue number2
DOIs
StatePublished - Apr 1995

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

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