On the number of permutation polynomials over a finite field

2013/10/29 by Kim, Kwang-Yon, Kim, Ryul · 1 citation
#11T06 #15A15 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1310.7691

Abstract

We find a formula for the number of permutation polynomials of degree q-2 over a finite field Fq, which has q elements, in terms of the permanent of a matrix. We write down an expression for the number of permutation polynomials of degree q-2 over a finite field Fq, using the permanent of a matrix whose entries are pth roots of unity and using this obtain a nontrivial bound for the number. Finally, we provide a formula for the number of permutation polynomials of degree d less than q-2.

Cited by

• An algebraic approach to Latin squares of prime power order by local permutation polynomials

Related

• Enumerating Permutation Polynomials over finite fields by degree
• Further results on some classes of permutation polynomials over finite fields
• Further Results on Permutation Polynomials over Finite Fields
• Specific permutation polynomials over finite fields
• Permutation and local permutation polynomial of maximum degree