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arXiv · 1209.1880

On the Möbius function of the locally finite poset associated with a numerical semigroup

Jonathan Chappelon·Jorge Ramírez Alfonsín
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Abstract

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{ö}bius function associated to $\left(\mathbb{Z},\leqslant\_S\right)$ when $S$ is an arithmetic semigroup.

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Jonathan Chappelon, Jorge Ramírez Alfonsín. 2016-03-31. On the Möbius function of the locally finite poset associated with a numerical semigroup. https://doi.org/10.1007/s00233-012-9458-3

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