Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Permutation polynomials: iteration of shift and inversion maps over
  finite fields   We show that all permutations in $S_n$ can be generated by affine unicritical
polynomials. We use the $\operatorname{PGL}$ 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.

23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph