The numerical duplication of a numerical semigroup

Abstract

In this paper we present and study the numerical duplication of a numerical semigroup, a construction that, starting with a numerical semigroup S and a semigroup ideal E ⊆ S, produces a new numerical semigroup, denoted by S ⋊ ⋉ b E (where b is any odd integer belonging to S), such that S = (S ⋊ ⋉ b E)/2. In particular, we characterize the ideals E such that S ⋊ ⋉ b E is almost symmetric and we determine its type. MSC: 20M14; 13H10.