Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Bounds on Lattice Covering Densities of Simplices   This paper presents new lower bounds for the lattice covering densities of
simplices by studying the Degree-Diameter Problem for abelian Cayley digraphs.
In particular, it proves that the density of any lattice covering of a
tetrahedron is at least $25/18$ and the density of any lattice covering of a
four-dimensional simplex is at least $343/264$.

6
The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex