Numerical semigroups: Apéry sets and Hilbert series

Abstract

Let a1,…,an be relatively prime positive integers, and let S be the semigroup consisting of all non-negative integer linear combinations of a1,…,an. In this paper, we focus our attention on AA-semigroups, that is semigroups being generated by almost arithmetic progressions. After some general considerations, we give a characterization of the symmetric AA-semigroups. We also present an efficient method to determine an Apery set and the Hilbert series of an AA-semigroup.