  In this paper we analyze the irreducibility of numerical semigroups with
multiplicity up to four. Our approach uses the notion of Kunz-coordinates
vector of a numerical semigroup recently introduced in (Blanco-Puerto, 2011).
With this tool we also completely describe the whole family of minimal
decompositions into irreducible numerical semigroups with the same multiplicity
for this set of numerical semigroups. We give detailed examples to show the
applicability of the methodology and conditions for the irreducibility of
well-known families of numerical semigroups as those that are generated by a
generalized arithmetic progression.

Commutative Algebra;Combinatorics;Number Theory