Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar semilattices and nearlattices with eighty-three subnearlattices   Finite (upper) nearlattices are essentially the same mathematical entities as
finite semilattices, finite commutative idempotent semigroups, finite
join-enriched meet semilattices, and chopped lattices. We prove that if an
$n$-element nearlattice has at least $83\cdot 2^{n-8}$ subnearlattices, then it
has a planar Hasse diagram. For $n>8$, this result is sharp.

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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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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: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an