Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Representability of Integers as $2$-Sums   A set $\mathcal{A}$ is said to be an additive $h$-basis if each element in
$\{0,1,\ldots,hn\}$ can be written as an $h$-sum of elements of $\mathcal{A}$
in {\it at least} one way. We seek multiple representations as $h$-sums, and,
in this paper we make a start by restricting ourselves to $h=2$. We say that
$\mathcal{A}$ is said to be a truncated $(\alpha,2,g)$ additive basis if each
$j\in[\alpha n, (2-\alpha)n]$ can be represented as a $2$-sum of elements of
$\mathcal{A}$ in at least $g$ ways. In this paper, we provide sharp asymptotics
for the event that a randomly selected set is a truncated $(\alpha,2,g)$
additive basis with high or low probability.

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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas