Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Direct and inverse results on restricted signed sumsets in integers   Let $G$ be an additive abelian group. Let $A=\{a_{0}, a_{1},\ldots,
a_{k-1}\}$ be a nonempty finite subset of $G$. For a positive integer $h$
satisfying $1\leq h\leq k$, we let
\[h\hat{}_{\underline{+}}A:=\{\Sigma_{i=0}^{k-1}\lambda_{i} a_{i}:
(\lambda_{0},\lambda_{1}, \ldots, \lambda_{k-1}) \in
\{-1,0,1\}^{k},~\Sigma_{i=0}^{k-1}|\lambda_{i}|=h \},\] be the restricted
signed sumset of $A$. The direct problem for the restricted signed sumset
$h\hat{}_{\underline{+}}A$ is to find the minimum number of elements in
$h\hat{}_{\underline{+}}A$ in terms of $|A|$. The inverse problem for
$h\hat{}_{\underline{+}}A$ is to determine the structure of the finite set $A$
for which $|h\hat{}_{\underline{+}}A|$ is minimal. In this article, we solve
some cases of both direct and inverse problems for $h\hat{}_{\underline{+}}A$,
when $A$ is a finite set of integers. In this connection, we also pose some
questions as conjectures in the remaining cases.

28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn