On the elasticity of a numerical semigroup.

Abstract

Let S be a numerical semigroup, and msg(S) its minimal system of generators. Then m(S) = min(msg(S)), M(S) = max(msg(S)), e(S), which is the cardinality of msg(S), and S (S) = M(S) m(S) , are called the multiplicity, comultiplicity, embedding dimension, and elasticity of S, respectively. Let m and M be positive integers, and let q be a rational number greater than 1. In this paper, we will study the following sets: • {S | S is a numerical semigroup, m(S) = m and M(S) = M}, • {S | S is a numerical semigroup, m(S) = m and S (S) ≤ q}, and • {S | S is a numerical semigroup, e(S) = 3 and S (S) = q}.