Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Permutation and extension for planar quasi-independent subsets of the
  roots of unity   Let $e^{2\pi i\Q}$ denote the set of roots of unity. We consider subsets
$E\subset e^{2\pi i\Q}$ that are quasi-independent or algebraically independent
(as subsets of the discrete plane). A bijective map on $e^{2\pi i\Q}$ preserves
the algebraically independent sets iff it preserves the quasi-independent sets,
and those maps are characterized. The effect on the size of quasi-independent
sets in the $n^{th}$ roots of unity $Z_n$ of increasing a prime factor of $n$
is studied.

24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
1
The categories of this paper are: cs
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an