Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the M\"obius function of the locally finite poset associated with a
  numerical semigroup   Let $S$ be a numerical semigroup and let
$\left(\mathbb{Z},\leqslant\_S\right)$ be the (locally finite) poset induced by
$S$ on the set of integers $\mathbb{Z}$ defined by $x \leqslant\_S y$ if and
only if $y-x\in S$ for all integers $x$ and $y$. In this paper, we investigate
the M{\"o}bius function associated to $\left(\mathbb{Z},\leqslant\_S\right)$
when $S$ is an arithmetic semigroup.

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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: q-bio