Enumerating transformation semigroups

James East, Attila Egri-Nagy*, James D. Mitchell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)109-125
Number of pages17
JournalSemigroup Forum
Issue number1
Early online date3 Apr 2017
Publication statusPublished - Aug 2017


  • Computational enumeration
  • Ideal structure
  • Multiplication table
  • Transformation semigroup


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