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Mathematics of Computation

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Computation of numerical semigroups by means of seeds

Authors: Maria Bras-Amorós and Julio Fernández-González
Journal: Math. Comp. 87 (2018), 2539-2550
MSC (2010): Primary 06F05, 20M14; Secondary 05A15, 68W30
Published electronically: January 8, 2018
MathSciNet review: 3802445
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Abstract: For the elements of a numerical semigroup which are larger than the Frobenius number, we introduce the definition of seed by broadening the notion of generator. This new concept allows us to explore the semigroup tree in an alternative efficient way, since the seeds of each descendant can be easily obtained from the seeds of its parent. The paper is devoted to presenting the results which are related to this approach, leading to a new algorithm for computing and counting the semigroups of a given genus.

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Maria Bras-Amorós
Affiliation: Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avinguda dels Països Catalans, 26, E-43007 Tarragona

Julio Fernández-González
Affiliation: Departament de Matemàtiques, Universitat Politècnica de Catalunya, EPSEVG – Avinguda Víctor Balaguer, 1, E-08800 Vilanova i la Geltrú

Received by editor(s): July 1, 2016
Received by editor(s) in revised form: March 29, 2017
Published electronically: January 8, 2018
Additional Notes: The first author was supported by the Spanish government under grant TIN2016-80250-R and by the Catalan government under grant 2014 SGR 537
The second author was partially supported by the Spanish government under grant MTM2015-66180-R
Article copyright: © Copyright 2018 American Mathematical Society