Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of nilpotent semigroups of degree 3   A semigroup is \emph{nilpotent} of degree 3 if it has a zero, every product
of 3 elements equals the zero, and some product of 2 elements is non-zero. It
is part of the folklore of semigroup theory that almost all finite semigroups
are nilpotent of degree 3.
  We give formulae for the number of nilpotent semigroups of degree 3 with
$n\in\N$ elements up to equality, isomorphism, and isomorphism or
anti-isomorphism. Likewise, we give formulae for the number of nilpotent
commutative semigroups with $n$ elements up to equality and up to isomorphism.

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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc