%0 Journal Article 
%A Moreno Frías, María Ángeles
%A Rosales, José Carlos
%T Counting the numerical semigroups with a specific special gap
%D 2022
%@ 1532-4125

%U http://hdl.handle.net/10498/35536
%X Let S be a numerical semigroup. An element x ∈  N\S is a special gap of S
if S ­∪{x} is also a numerical semigroup. If a is a positive integer, we
denote by A(a) the set of all numerical semigroups for which a is a special
gap. We say that an element of A(a) is A(a)-irreducible if it cannot
be expressed as the intersection of two numerical semigroups of A(a),
properly containing it. The main aim of this paper is to describe three
algorithmic procedures: the first one calculates the elements of A(a), the
second one determines whether or not a numerical semigroup is
A(a)-irreducible and the third one computes all the A(a)-irreducibles
numerical semigroups.
%K A(a)-irreducible numerical semigroup
%K ANI-semigroup
%K atomic numerical semigroup
%K Frobenius number
%K gap
%K genus
%K irreducible numerical semigroup
%~ Universidad de Cádiz