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Mathematics of Computation

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The right-generators descendant of a numerical semigroup


Authors: Maria Bras-Amorós and Julio Fernández-González
Journal: Math. Comp. 89 (2020), 2017-2030
MSC (2010): Primary 06F05, 20M14; Secondary 05A99, 68W30
DOI: https://doi.org/10.1090/mcom/3502
Published electronically: January 15, 2020
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Abstract: For a numerical semigroup, we encode the set of primitive elements that are larger than its Frobenius number and show how to produce in a fast way the corresponding sets for its children in the semigroup tree. This allows us to present an efficient algorithm for exploring the tree up to a given genus. The algorithm exploits the second nonzero element of a numerical semigroup and the particular pseudo-ordinary case in which this element is the conductor.


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Additional Information

Maria Bras-Amorós
Affiliation: Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avinguda dels Països Catalans, 26, E-43007 Tarragona, Spain
Email: maria.bras@urv.cat

Julio Fernández-González
Affiliation: Departament de Matemàtiques, Universitat Politècnica de Catalunya, EPSEVG – Avinguda Víctor Balaguer, 1, E-08800 Vilanova i la Geltrú, Barcelona, Spain
Email: julio.fernandez.g@upc.edu

DOI: https://doi.org/10.1090/mcom/3502
Received by editor(s): June 3, 2019
Received by editor(s) in revised form: June 14, 2019, and October 28, 2019
Published electronically: January 15, 2020
Additional Notes: The first author was supported by the Spanish government under grant TIN2016-80250-R and by the Catalan government under grant 2017 SGR 00705
The second author was partially supported by the Spanish government under grant MTM2015-66180-R
Article copyright: © Copyright 2020 American Mathematical Society