Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Minimum Size of Signed Sumsets in Elementary Abelian Groups   For a finite abelian group $G$ and positive integers $m$ and $h$, we let
$$\rho(G, m, h) = \min \{|hA| \; : \; A \subseteq G, |A|=m\}$$ and $$\rho_{\pm}
(G, m, h) = \min \{|h_{\pm} A| \; : \; A \subseteq G, |A|=m\},$$ where $hA$ and
$h_{\pm} A$ denote the $h$-fold sumset and the $h$-fold signed sumset of $A$,
respectively. The study of $\rho(G, m, h)$ has a 200-year-old history and is
now known for all $G$, $m$, and $h$. In previous work we provided an upper
bound for $\rho_{\pm} (G, m, h)$ that we believe is exact, and proved that
$\rho_{\pm} (G, m, h)$ agrees with $\rho (G, m, h)$ when $G$ is cyclic. Here we
study $\rho_{\pm} (G, m, h)$ for elementary abelian groups $G$; in particular,
we determine all values of $m$ for which $\rho_{\pm} (\mathbb{Z}_p^2, m, 2)$
equals $\rho (\mathbb{Z}_p^2, m, 2)$ for a given prime $p$.

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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc