The enumeration of the set of atomic numerical semigroups with fixed Frobenius number-Reference-Cited by-同舟云学术

The enumeration of the set of atomic numerical semigroups with fixed Frobenius number

Published:2019-07-25 Issue:08 Volume:19 Page:2050144
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Robles-Pérez Aureliano M.¹,Rosales José Carlos²

Affiliation:

1. Departamento de Matemática Aplicada, Universidad de Granada E-18071 Granada, España

2. Departamento de Álgebra Universidad de Granada, E-18071 Granada, España

Abstract

A numerical semigroup is irreducible if it cannot be obtained as an intersection of two numerical semigroups containing it properly. If we only consider numerical semigroups with the same Frobenius number, that concept is generalized to atomic numerical semigroup. Based on a previous one developed to obtain all irreducible numerical semigroups with a fixed Frobenius number, we present an algorithm for computing all atomic numerical semigroups with a fixed Frobenius number.

Funder

Ministerio de Ciencia, Innovacion y Universidades

Fondo Europeo de Desarrollo Regional FEDER

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498820501443

Reference9 articles.

1. On the enumeration of the set of numerical semigroups with fixed Frobenius number

2. The tree of irreducible numerical semigroups with fixed Frobenius number

3. On numerical semigroups

4. The value-semigroup of a one-dimensional Gorenstein ring

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