Enumerating transformation semigroups

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

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Date

08/2017

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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).

Collections

University of St Andrews Research

URL

https://arxiv.org/abs/1403.0274

URI

http://hdl.handle.net/10023/13064