The Covariety of Bracelet numerical semigroups with fixed Frobenius number

Abstract

Given a set of positive integers {n1,…,np}, we say that a numerical semigroup S is a {n1,…,np}-bracelet if a+b+{n1,…,np}⊆S for every a,b∈S∖{0}. In this note we study the set of {n1,…,np}-bracelet numerical semigroups with fixed Frobenius number, denoted by B({n1,…,np},F). We will prove that B({n1,…,np},F) is a covariety and we will give algorithms for computing all elements in B({n1,…,np},F) or all elements in B({n1,…,np},F) with fixed genus.