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

Jonathan Chappelon (1) , Jorge Luis Ramírez Alfonsín (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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 Möbius function associated to $\left(\mathbb{Z},\leqslant_S\right)$ when $S$ is an arithmetic semigroup.

Mots clés: Möbius function; poset; numerical semigroup; arithmetic semigroup

Domaines: Combinatoire [math.CO]

Jonathan Chappelon, Jorge Luis Ramírez Alfonsín. On the Möbius function of the locally finite poset associated with a numerical semigroup. Semigroup Forum, 2013, 87 (2), pp.313-330. ⟨10.1007/s00233-012-9458-3⟩. ⟨hal-00730229v3⟩