Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A power sum formula by Carlitz and its applications to permutation
  rational functions of finite fields   A formula discovered by L. Carlitz in 1935 finds an interesting application
in permutation rational functions of finite fields. It allows us to determine
all rational functions of degree three that permute the projective line $\Bbb
P^1(\Bbb F_q)$ over $\Bbb F_q$, a result previously obtained by Ferraguti and
Micheli through a different method. It also allows us to determine all rational
functions of degree four that permute $\Bbb P^1(\Bbb F_q)$ under a certain
condition. (A complete determination of all rational functions of degree four
that permute $\Bbb P^1(\Bbb F_q)$ without any condition will appear in a
separate forthcoming paper.)

15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys