On permutation polynomials over finite fields. (1987)

• Record Type: Journal Article
• Authors: Mollin, R. A.; Small, C.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 10:Number 3(1987)
• Page Start: 535
• Page End: 543
• Publication Date: 1987
• Subjects: polynomials -- irreducibility -- factorization -- distribution of values; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171287000644
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : A polynomialf over a finite fieldF is called a permutation polynomial if the mappingF → F defined byf is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integerm, the cardinality of finite fields admitting permutation polynomials of degreem is bounded.