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Towards a better understanding of the semigroup tree

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Abstract

In this paper we elaborate on the structure of the semigroup tree and the regularities on the number of descendants of each node observed earlier by the first author. These regularities admit two different types of behavior and in this work we investigate which of the two types takes place for some well-known classes of semigroups. Also we study the question of what kind of chains appear in the tree and characterize the properties (like being (in)finite) thereof. We conclude with some thoughts that show how this study of the semigroup tree may help in solving the conjecture of Fibonacci-like behavior of the number of semigroups with given genus.

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Authors and Affiliations

  1. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007, Tarragona, Catalonia, Spain

    Maria Bras-Amorós

  2. Department of Secure Data, Center for Advanced Security Research Darmstadt, Mornewegstrasse 32, 64293, Darmstadt, Germany

    Stanislav Bulygin

Authors
  1. Maria Bras-Amorós
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  2. Stanislav Bulygin
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Corresponding author

Correspondence to Maria Bras-Amorós.

Additional information

Communicated by Jorge Almeida.

This work was partly supported by the Spanish Government through projects TSI2007-65406-C03-01 “E-AEGIS” and CONSOLIDER INGENIO 2010 CSD2007-00004 “ARES”, and by the Government of Catalonia under grant 2009 SGR 1135.

The second author was partially funded by the DASMOD Cluster of Excellence in Rheinland-Palatinate.

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Bras-Amorós, M., Bulygin, S. Towards a better understanding of the semigroup tree. Semigroup Forum 79, 561–574 (2009). https://doi.org/10.1007/s00233-009-9175-8

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  • DOI: https://doi.org/10.1007/s00233-009-9175-8

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