Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Erd\H{o}s-Ginzburg-Ziv constants by avoiding three-term arithmetic
  progressions   For a finite abelian group $G$, the Erd\H{o}s-Ginzburg-Ziv constant
$\mathfrak{s}(G)$ is the smallest $s$ such that every sequence of $s$ (not
necessarily distinct) elements of $G$ has a zero-sum subsequence of length
$\operatorname{exp}(G)$. For a prime $p$, let $r(\mathbb{F}_p^n)$ denote the
size of the largest subset of $\mathbb{F}_p^n$ without a three-term arithmetic
progression. Although similar methods have been used to study $\mathfrak{s}(G)$
and $r(\mathbb{F}_p^n)$, no direct connection between these quantities has
previously been established. We give an upper bound for $\mathfrak{s}(G)$ in
terms of $r(\mathbb{F}_p^n)$ for the prime divisors $p$ of
$\operatorname{exp}(G)$. For the special case $G=\mathbb{F}_p^n$, we prove
$\mathfrak{s}(\mathbb{F}_p^n)\leq 2p\cdot r(\mathbb{F}_p^n)$. Using the upper
bounds for $r(\mathbb{F}_p^n)$ of Ellenberg and Gijswijt, this result improves
the previously best known upper bounds for $\mathfrak{s}(\mathbb{F}_p^n)$ given
by Naslund.

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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph