English

On the number of permutation polynomials over a finite field

Rings and Algebras 2013-12-18 v2

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.

Keywords

Cite

@article{arxiv.1310.7691,
  title  = {On the number of permutation polynomials over a finite field},
  author = {Kwang-Yon Kim and Ryul Kim},
  journal= {arXiv preprint arXiv:1310.7691},
  year   = {2013}
}

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10 pages