Semigroup Forum

, Volume 95, Issue 1, pp 109–125 | Cite as

Enumerating transformation semigroups

Research Article

Abstract

We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation semigroups up to degree 4. Classification of these semigroups up to conjugacy, isomorphism and anti-isomorphism, by size and rank, provides a solid base for further investigations of transformation semigroups.

Keywords

Transformation semigroup Computational enumeration Multiplication table Ideal structure 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • James East
    • 1
  • Attila Egri-Nagy
    • 2
  • James D. Mitchell
    • 3
  1. 1.School of Computing, Engineering and Mathematics, Centre for Research in MathematicsUniversity of Western Sydney (Parramatta Campus)PenrithAustralia
  2. 2.Akita International UniversityYuwa, Akita-CityJapan
  3. 3.Mathematical InstituteUniversity of St AndrewsFifeScotland, UK

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