Counting the numerical semigroups with a specific special gap

Let S be a numerical semigroup. An element is a special gap of S if is also a numerical semigroup. If a is a positive integer, we denote by the set of all numerical semigroups for which a is a special gap. We say that an element of is -irreducible if it cannot be expressed as the intersection of two...

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Published in:Communications in algebra 2022-12, Vol.50 (12), p.5132-5144
Main Authors: Moreno-Frías, M. A., Rosales, J. C.
Format: Article
Language:English
Subjects:
(a)-irreducible numerical semigroup
ANI-semigroup
atomic numerical semigroup
Frobenius number
gap
genus
irreducible numerical semigroup
Primary: 20M14
Secondary: 11Y16
Semigroups
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Rosales, J. C.
description Let S be a numerical semigroup. An element is a special gap of S if is also a numerical semigroup. If a is a positive integer, we denote by the set of all numerical semigroups for which a is a special gap. We say that an element of is -irreducible if it cannot be expressed as the intersection of two numerical semigroups of properly containing it. The main aim of this paper is to describe three algorithmic procedures: the first one calculates the elements of the second one determines whether or not a numerical semigroup is -irreducible and the third one computes all the -irreducibles numerical semigroups.
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subjects (a)-irreducible numerical semigroup
ANI-semigroup
atomic numerical semigroup
Frobenius number
gap
genus
irreducible numerical semigroup
Primary: 20M14
Secondary: 11Y16
Semigroups
title Counting the numerical semigroups with a specific special gap
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