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International Conference on Principles and Practice of Constraint Programming

CP 2012: Principles and Practice of Constraint Programming pp 883–899Cite as

The Semigroups of Order 10

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7514))

Abstract

The number of finite semigroups increases rapidly with the number of elements. Since existing counting formulae do not give the complete number of semigroups of given order up to equivalence, the remainder can only be found by careful search. We describe the use of mathematical results combined with distributed Constraint Satisfaction to show that the number of non-equivalent semigroups of order 10 is 12,418,001,077,381,302,684. This solves a previously open problem in Mathematics, and has directly led to improvements in Constraint Satisfaction technology.

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Author information

Authors and Affiliations

  1. Centro de Álgebra da Universidade de Lisboa, 1649-003, Lisboa, Portugal

    Andreas Distler

  2. School of Computer Science, University of St. Andrews, KY16 9SX, UK

    Chris Jefferson, Tom Kelsey & Lars Kotthoff

Authors
  1. Andreas Distler
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  2. Chris Jefferson
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  3. Tom Kelsey
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  4. Lars Kotthoff
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Editor information

Editors and Affiliations

  1. DEIS Universitá di Bologna, V.le Risorgimento, 2, 40136, Bologna, Italy

    Michela Milano

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Distler, A., Jefferson, C., Kelsey, T., Kotthoff, L. (2012). The Semigroups of Order 10. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_63

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  • DOI: https://doi.org/10.1007/978-3-642-33558-7_63

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33557-0

  • Online ISBN: 978-3-642-33558-7

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