Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The rectilinear local crossing number of $K_n$   We determine ${\bar{\rm{lcr}}}(K_n)$, the rectilinear local crossing number
of the complete graph $K_n$ for every $n$. More precisely, for every $n \notin
\{8, 14 \}, $ \[ {\bar{\rm{lcr}}}(K_n)=\left\lceil \frac{1}{2} \left(
n-3-\left\lceil \frac{n-3}{3} \right\rceil \right) \left\lceil \frac{n-3}{3}
\right\rceil \right\rceil, \] ${\bar{\rm{lcr}}}(K_8)=4$, and
${\bar{\rm{lcr}}}(K_{14})=15$.

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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys