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Enumerating transformation semigroups

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SemigroupForum_1403.0274_AM.pdf (410.8Kb)
Date
08/2017
Author
East, James
Egri-Nagy, Attila
Mitchell, James D.
Keywords
Computational enumeration
Ideal structure
Multiplication table
Transformation semigroup
QA Mathematics
Algebra and Number Theory
T-NDAS
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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.
Citation
East , J , Egri-Nagy , A & Mitchell , J D 2017 , ' Enumerating transformation semigroups ' , Semigroup Forum , vol. 95 , no. 1 , pp. 109-125 . https://doi.org/10.1007/s00233-017-9869-2
Publication
Semigroup Forum
Status
Peer reviewed
DOI
https://doi.org/10.1007/s00233-017-9869-2
ISSN
0037-1912
Type
Journal article
Rights
Copyright © 2017, Springer Science+Business Media New York This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1007/s00233-017-9869-2
Description
This work was partially supported by the NeCTAR Research Cloud, an initiative of the Australian Government’s Super Science scheme and the Education Investment Fund; and by the EU Project BIOMICS (Contract Number CNECT-ICT-318202).
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  • University of St Andrews Research
URL
https://arxiv.org/abs/1403.0274
URI
http://hdl.handle.net/10023/13064

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