Numerical Semigroups with a Fixed Fundamental Gap

María Ángeles Moreno-Frías () and José Carlos Rosales
Additional contact information
María Ángeles Moreno-Frías: Department of Mathematics, Faculty of Sciences, University of Cádiz, E-11510 Puerto Real, Spain
José Carlos Rosales: Department of Algebra, Faculty of Sciences, University of Granada, E-18071 Granada, Spain

Mathematics, 2024, vol. 13, issue 1, 1-13

Abstract: A gap a of a numerical semigroup S is fundamental if { 2 a , 3 a } ⊆ S . In this work, we will study the set B ( a ) = S ∣ S is a numerical semigroup and a is a fundamental gap of S . 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 ) .

Keywords: numerical semigroup; monoids; fundamental gap; genus; Frobenius number; algorithm; B ( a ) -rank (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/1/95/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/1/95/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2024:i:1:p:95-:d:1555859

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().