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

Abstract

Let $S$ be a numerical semigroup and let $\left(\mathbb{Z},⩽\_S\right)$ be the (locally finite) poset induced by $S$ on the set of integers $\mathbb{Z}$ defined by $x⩽\_Sy$ 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 $\left(\mathbb{Z},⩽\_S\right)$ when $S$ is an arithmetic semigroup.

15 pages ; 1 table

Cited by in corpus (2)

• numericalsgps, a GAP package for numerical semigroups
• Möbius function of semigroup posets through Hilbert series