Möbius function of semigroup posets through Hilbert series

Abstract

In this paper, we investigate the M{ö}bius function $\mu \_\mathcal{S}$ associated to a (locally finite) poset arising from a semigroup $\mathcal{S}$ of ${\mathbb{Z}}^m$. We introduce and develop a new approach to study $\mu \_\mathcal{S}$ by using the Hilbert series of $\mathcal{S}$. The latter enables us to provide formulas for $\mu \_\mathcal{S}$ when $\mathcal{S}$ belongs to certain families of semigroups. Finally, a characterization for a locally finite poset to be isomorphic to a semigroup poset is given.

11 pages

References in corpus (3)

• Affine semigroups having a unique Betti element
• On the Möbius function of the locally finite poset associated with a numerical semigroup
• Complete intersections in simplicial toric varieties