Enumerating Transformation Semigroups
arXiv:1403.0274
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.
11 pages, 6 figures, 3 tables, v4: updated references,added T4 gap values, corrections in examples