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Mathematics of Computation

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Exploring the tree of numerical semigroups


Authors: Jean Fromentin and Florent Hivert
Journal: Math. Comp. 85 (2016), 2553-2568
MSC (2010): Primary 05A15, 68R05, 68W10
DOI: https://doi.org/10.1090/mcom/3075
Published electronically: December 31, 2015
MathSciNet review: 3511292
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Abstract: In this paper we describe an algorithm visiting all numerical semigroups up to a given genus using a well-suited representation. The interest of this algorithm is that it fits particularly well the architecture of modern computers allowing very large optimizations: we obtain the number of numerical semigroups of genus $ g\leq 67$ and we confirm the Wilf conjecture for $ g\leq 60$.


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Additional Information

Jean Fromentin
Affiliation: Univ. Littoral Côte d’Opale, EA 2597 - LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville, F-62228 Calais, France
Email: fromentin@lmpa.univ-littoral.fr

Florent Hivert
Affiliation: Laboratoire de Recherche Informatique (UMR CNRS 8623), Université Paris Sud, Université Paris-Saclay, Bureau 33, Bât 650 Ada Lovelace, Université Paris Sud Rue Noetzlin, 91190 Gif-sur-Yvette
Email: florent.hivert@lri.fr

DOI: https://doi.org/10.1090/mcom/3075
Received by editor(s): November 3, 2014
Received by editor(s) in revised form: April 10, 2015
Published electronically: December 31, 2015
Article copyright: © Copyright 2015 American Mathematical Society