Enumerating transformation semigroups

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

doi:10.1007/s00233-017-9869-2

Enumerating transformation semigroups

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	109-125
Number of pages	17
Journal	Semigroup Forum
Volume	95
Issue number	1
Early online date	3 Apr 2017
DOIs	https://doi.org/10.1007/s00233-017-9869-2
Publication status	Published - Aug 2017

Keywords

Computational enumeration
Ideal structure
Multiplication table
Transformation semigroup

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10.1007/s00233-017-9869-2

SemigroupForum_1403.0274_AM
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
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https://arxiv.org/abs/1403.0274

Cite this

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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.",

keywords = "Computational enumeration, Ideal structure, Multiplication table, Transformation semigroup",

author = "James East and Attila Egri-Nagy and Mitchell, {James D.}",

note = "This work was partially supported by the NeCTAR Research Cloud, an initiative of the Australian Government{\textquoteright}s Super Science scheme and the Education Investment Fund; and by the EU Project BIOMICS (Contract Number CNECT-ICT-318202).",

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N2 - 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.

AB - 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.

KW - Computational enumeration

KW - Ideal structure

KW - Multiplication table

KW - Transformation semigroup

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Enumerating transformation semigroups

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Keywords

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