Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting sum-free sets in Abelian groups   In this paper we study sum-free sets of order $m$ in finite Abelian groups.
We prove a general theorem on 3-uniform hypergraphs, which allows us to deduce
structural results in the sparse setting from stability results in the dense
setting. As a consequence, we determine the typical structure and asymptotic
number of sum-free sets of order $m$ in Abelian groups $G$ whose order is
divisible by a prime $q$ with $q \equiv 2 \pmod 3$, for every $m \ge C(q)
\sqrt{n \log n}$, thus extending and refining a theorem of Green and Ruzsa. In
particular, we prove that almost all sum-free subsets of size $m$ are contained
in a maximum-size sum-free subset of $G$. We also give a completely
self-contained proof of this statement for Abelian groups of even order, which
uses spectral methods and a new bound on the number of independent sets of size
$m$ in an $(n,d,\lambda)$-graph.

32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
1
The categories of this paper are: cs
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat