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On the M\"obius function of the locally finite poset associated with a numerical semigroup

Authors
  • Chappelon, Jonathan
  • Alfonsín, Jorge Ramírez
Type
Published Article
Publication Date
Mar 31, 2016
Submission Date
Sep 10, 2012
Identifiers
DOI: 10.1007/s00233-012-9458-3
Source
arXiv
License
Yellow
External links

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

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