English

Permutation polynomials: iteration of shift and inversion maps over finite fields

Number Theory 2021-03-22 v2

Abstract

We show that all permutations in SnS_n can be generated by affine unicritical polynomials. We use the PGL\operatorname{PGL} group structure to compute the cycle structure of permutations with low Carlitz rank. The tree structure of the group generated by shift and inversion maps is used to study the randomness properties of permutation polynomials.

Keywords

Cite

@article{arxiv.1910.12928,
  title  = {Permutation polynomials: iteration of shift and inversion maps over finite fields},
  author = {Anna Chlopecki and Juliano Levier-Gomes and Wayne Peng and Alex Shearer and Adam Towsley},
  journal= {arXiv preprint arXiv:1910.12928},
  year   = {2021}
}
R2 v1 2026-06-23T11:57:40.207Z