Delta sets for nonsymmetric numerical semigroups with embedding dimension three
type: Item
instance of: scholarly article
title: Delta sets for nonsymmetric numerical semigroups with embedding dimension three
zbMATH Open document ID: 1458.20048
author: D. Llena
author: Alessio Moscariello
author: Pedro A. García Sánchez
published in: Forum Mathematicum
publication date: 2018-01-12T00:00:00Z
review text: Let \(S\) be a nonsymmetric numerical semigroup with embedding dimension three. In this paper, the authors define the Bézout couples, generate a semigroup with them and use them in order to give the Delta set of \(S\). Moreover, a fast algorithm for computing this invariant is given. They compare their algorithm with the previous one implemented in GAP getting a huge difference of time. Finally, they solve the question `which finite subsets of \(\mathbb{N}\) are admissible Delta set for embedding dimension three numerical semigroups?'.
reviewed by: Daniel Marín Aragon
Mathematics Subject Classification ID: 20M13
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 6825353
zbMATH Keywords: numerical semigroup
zbMATH Keywords: factorizations
zbMATH Keywords: delta sets
zbMATH Keywords: symmetric numerical semigroup
zbMATH Keywords: Euclid's algorithm
describes a project that uses: numericalsgps
describes a project that uses: GAP
MaRDI profile type: Publication
full work available at URL: forum-2015-0065
OpenAlex ID: W2568727823
cites work: An algorithm to compute the primitive elements of an embedding dimension three numerical semigroup.
cites work: On dynamic algorithms for factorization invariants in numerical monoids
cites work: ON DELTA SETS OF NUMERICAL MONOIDS
cites work: On the delta set and the Betti elements of a BF-monoid.
cites work: Delta sets of numerical monoids are eventually periodic.
cites work: Delta Sets of Numerical Monoids Using Nonminimal Sets of Generators
cites work: Shifts of generators and delta sets of numerical monoids.
cites work: The realization problem for delta sets of numerical semigroups
cites work: numericalsgps, a GAP package for numerical semigroups
cites work: Computation of delta sets of numerical monoids.
cites work: An Overview of the Computational Aspects of Nonunique Factorization Invariants
cites work: On the arithmetic of certain not integrally closed noetheian integral domains
cites work: A Linear Diophantine Problem
cites work: Numerical semigroups.
DOI: 10.1515/FORUM-2015-0065
description: scientific article; zbMATH DE number 6825353