Enumerating Transformation Semigroups
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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2014
- DOI:
- 10.48550/arXiv.1403.0274
- arXiv:
- arXiv:1403.0274
- Bibcode:
- 2014arXiv1403.0274E
- Keywords:
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- Mathematics - Group Theory;
- 20M20
- E-Print:
- 11 pages, 6 figures, 3 tables, v4: updated references,added T4 gap values, corrections in examples