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

Western Sydney University

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

5 Citations (Scopus)

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
DOIs	https://doi.org/10.1007/s00233-017-9869-2
Publication status	Published - 1 Aug 2017

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media New York.

Keywords

algorithms
multiplication
semigroups

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10.1007/s00233-017-9869-2

Cite this

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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 - algorithms

KW - multiplication

KW - semigroups

UR - http://handle.westernsydney.edu.au:8081/1959.7/uws:39966

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JO - Semigroup Forum

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Enumerating transformation semigroups

Abstract

Bibliographical note

Keywords

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