Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cut-and-project quasicrystals, lattices, and dense forests   Dense forests are discrete subsets of Euclidean space which are uniformly
close to all sufficiently long line segments. The degree of density of a dense
forest is measured by its visibility function. We show that cut-and-project
quasicrystals are never dense forests, but their finite unions could be
uniformly discrete dense forests. On the other hand, we show that finite unions
of lattices typically are dense forests, and give a bound on their visibility
function, which is close to optimal. We also construct an explicit finite union
of lattices which is a uniformly discrete dense forest with an explicit bound
on its visibility.

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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: math-ph