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New Eliahou Semigroups and Verification of the Wilf Conjecture for Genus up to 65

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Modeling Decisions for Artificial Intelligence (MDAI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12898))

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Abstract

We give a graphical reinterpretation of the seeds algorithm to explore the tree of numerical semigroups. We then exploit the seeds algorithm to find all the Eliahou semigroups of genus up to 65. Since all these semigroups satisfy the Wilf conjecture, this shows that the Wilf conjecture holds up to genus 65.

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References

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Acknowledgment

The authors would like to thank Enric Pons Montserrat, Manuel Delgado, and Julio Fernández-González for their contribution in this work. This work was partly supported by the Catalan Government under grant 2017 SGR 00705 and by the Spanish Ministry of Economy and Competitivity under grant TIN2016-80250-R and grant RTI2018-095094-B-C21.

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Authors and Affiliations

  1. Universitat Rovira i Virgili, Tarragona, Spain

    Maria Bras-Amorós & César Marín Rodríguez

Authors
  1. Maria Bras-Amorós
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  2. César Marín Rodríguez
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Corresponding author

Correspondence to Maria Bras-Amorós .

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Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Vicenç Torra

  2. Tamagawa University, Tokyo, Japan

    Yasuo Narukawa

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Bras-Amorós, M., Rodríguez, C.M. (2021). New Eliahou Semigroups and Verification of the Wilf Conjecture for Genus up to 65. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2021. Lecture Notes in Computer Science(), vol 12898. Springer, Cham. https://doi.org/10.1007/978-3-030-85529-1_2

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  • DOI: https://doi.org/10.1007/978-3-030-85529-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85528-4

  • Online ISBN: 978-3-030-85529-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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