Bracelet monoids and numerical semigroups

Abstract

Given positive integers n1, . . . , n p, we say that a submonoid M of (N,+) is a (n1, . . . , n p)-bracelet if a +b+ n1, . . . , n p ⊆ M for every a, b ∈ M\ {0}. In this note, we explicitly describe the smallest n1, . . . , n p -bracelet that contains a finite subset X of N. We also present a recursive method that enables us to construct the whole set B(n1, . . . , n p) = M|M is a (n1, . . . , n p)-bracelet . Finally, we study (n1, . . . , n p)-bracelets that cannot be expressed as the intersection of (n1, . . . , n p)- bracelets properly containing it.