Numerical semigroups bounded by the translation of a plane monoid

Abstract

Let N be the set of nonnegative integer numbers. A plane monoid is a submonoid of (N2, +). Let M be a plane monoid and p, q ∈ N. We will say that an integer number n is M(p, q)-bounded if there is (a, b) ∈ M such that a + p ≤ n ≤ b − q. We will denote by A(M(p, q)) = {n ∈ N | n is M(p, q)-bounded}. An A(p, q)-semigroup is a numerical semigroup S such that S = A(M(p, q))∪{0} for some plane monoid M. In this work we will study these kinds of numerical semigroups.