Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-28T17:51:58.513Z Has data issue: false hasContentIssue false
  • English
  • Français

Dickson Polynomials of the Second Kind that are Permutations

Published online by Cambridge University Press:  20 November 2018

Stephen D. Cohen
Stephen D. Cohen*
Affiliation:
Department of Mathematics University of Glasgow Glasgow G12 8QW Scotland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is known that the Dickson polynomial of the second kind permutes the elements of the finite prime field (p odd) when n + 1 = ±2 to each of the moduli and . Based on numerical evidence it has been conjectured that these congruences are necessary for the polynomial to permute . The conjecture is established here by a new method

Keywords

11T06
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 2 , 01 April 1994 , pp. 225 - 238
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Brison, O. J., On group permutation polynomials, Portugal. Math. 50(1993), 365–383.Google Scholar
2. Fried, M. and Lidl, R., On Dickson polynomials and Rédei functions, Proc. Salzburg Conf., Contributions to General Algebra 5, Springer-Verlag Holder-Pichler-Tempsky, Wien, 1987, 139–149.Google Scholar
3. James, N. S. and Lidl, R., Permutation polynomials on matrices, Linear Algebra Appl. 96(1987), 181–190.Google Scholar
4. Lidl, R. and Mullen, G. L., When does a polynomial over a finite field permute the elements of the field?, Amer. Math. Monthly 95(1988), 243–246.Google Scholar
5. Lidl, R. and Niederreiter, H., Finite Fields, Encyclo. Math. Appls. 20, Addison-Wesley, Reading, Massachusetts, 1983.Google Scholar
6. Matthews, R. W., Permutation polynomials in one and several variables, Ph.D. Dissertation, University of Tasmania, 1982.Google Scholar
7. Mullen, G. L., Dickson polynomials over finite fields, Adv. in Math. (Beijing) 20(1991), 24–32.Google Scholar