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

G. L. Mullen

doi:10.1006/ffta.1995.1020

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

G. L. Mullen

Mathematics

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10 Scopus citations

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 F_p for infinitely many primes p. We also provide a survey of recent results concerning permutation polynomials over finite fields.

Original language	English (US)
Pages (from-to)	242-258
Number of pages	17
Journal	Finite Fields and their Applications
Volume	1
Issue number	2
DOIs	https://doi.org/10.1006/ffta.1995.1020
State	Published - Apr 1995

All Science Journal Classification (ASJC) codes

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

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10.1006/ffta.1995.1020

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

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.",

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AB - 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.

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

Abstract

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