The Frobenius problem for numerical semigroups
type: Item
instance of: scholarly article
title: The Frobenius problem for numerical semigroups
zbMATH Open document ID: 1262.11048
author: José Carlos Rosales
author: M. B. Branco
published in: Journal of Number Theory
publication date: 2011-10-21T00:00:00Z
review text: The paper provides a new method for computing the Frobenius number. The main idea of the method is the following. With the use of special projection any semigroup containing \(\langle n_1,n_2 \rangle\) can be characterized as a subset of incomparable elements of the set \[ B(n_1,n_2)=\{(a,b): 0<a<n_2, 0<b<n_1,\; n_1n_2-an_1-bn_2\geq0\}. \] Using this characterization the algorithm for computing of the Frobenius number of a numerical semigroup is presented. It should be mentioned that the method for the case of three dimensional numerical semigroup is formulated in terms of its minimal system of generators.
Mathematics Subject Classification ID: 11D07
Mathematics Subject Classification ID: 20M14
zbMATH DE Number: 5960854
zbMATH Keywords: Frobenius number
zbMATH Keywords: numerical semigroup
reviewed by: Dmitriy Frolenkov
describes a project that uses: NumericalSemigroupsWithGenus
MaRDI profile type: Publication
Wikidata QID: Q58842630
full work available at URL: j.jnt.2011.05.011
OpenAlex ID: W2022468054
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DOI: 10.1016/J.JNT.2011.05.011
description: scientific article; zbMATH DE number 5960854