Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simplices in thin subsets of Euclidean spaces   Let $\De$ be a non-degenerate simplex on $k$ vertices. We prove that there
exists a threshold $s_k<k$ such that any set $A\subs \R^k$ of Hausdorff
dimension $dim\,A\geq s_k$ necessarily contains a similar copy of the simplex
$\De$.

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The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
25
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: nucl-ex
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The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph