Year: 2024
Type: article
Abstract: A gap a of a numerical semigroup S is fundamental if {2a,3a}⊆S. In this work, we will study the set B(a)=S∣SisanumericalsemigroupandaisafundamentalgapofS. In particular, we will give an algorithm to compute all the elements of B(a) with a given genus. The intersection of two elements of B(a) is again one element of B(a). A B(a)-irreducible numerical semigroup is an element of B(a) that cannot be expressed as an intersection of two elements of B(a) containing it properly. In this paper, we will study the B(a)-irreducible numerical semigroups. In this sense we will give an algorithm to calculate all of them. Finally, we will study the submonoids of (N,+) that can be expressed as an intersection (finite or infinite) of elements belonging to B(a).
Source: Mathematics
DOI: 10.3390/math13010095
Institutions: Universidad de Cádiz, Universidad de Granada
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
Funder: Junta de Andalucía
Awards: G248826378, G763978806
OpenAlex ID: W4406018259