Generators and ranks in finite partial transformation semigroups

We extend the concept of path-cycle, to the semigroup Pn, of all partial maps on Xn={1,2,…,n}, and show that the classical decomposition of permutations into disjoint cycles can be extended to elements of Pn by means of path-cycles. The device is used to obtain information about generating sets for...

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Published in:Algebra and Discrete Mathematics
Date:2017
Main Authors: Garba, G.U., Imam, A.T.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2017
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/156026
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Generators and ranks in finite partial transformation semigroups / G.U. Garba, A.T. Imam // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 2. — С. 237-248. — Бібліогр.: 16 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Garba, G.U.
Imam, A.T.
author_facet Garba, G.U.
Imam, A.T.
citation_txt Generators and ranks in finite partial transformation semigroups / G.U. Garba, A.T. Imam // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 2. — С. 237-248. — Бібліогр.: 16 назв. — англ.
collection DSpace DC
container_title Algebra and Discrete Mathematics
description We extend the concept of path-cycle, to the semigroup Pn, of all partial maps on Xn={1,2,…,n}, and show that the classical decomposition of permutations into disjoint cycles can be extended to elements of Pn by means of path-cycles. The device is used to obtain information about generating sets for the semigroup Pn\Sn, of all singular partial maps of Xn. Moreover, we give a definition for the (m,r)-rank of Pn\Sn and show that it is n(n+1)/2.
first_indexed 2025-12-01T13:59:30Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1726-3255
language English
last_indexed 2025-12-01T13:59:30Z
publishDate 2017
publisher Інститут прикладної математики і механіки НАН України
record_format dspace
spelling Garba, G.U.
Imam, A.T.
2019-06-17T19:02:47Z
2019-06-17T19:02:47Z
2017
Generators and ranks in finite partial transformation semigroups / G.U. Garba, A.T. Imam // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 2. — С. 237-248. — Бібліогр.: 16 назв. — англ.
1726-3255
2010 MSC:20M20.
https://nasplib.isofts.kiev.ua/handle/123456789/156026
We extend the concept of path-cycle, to the semigroup Pn, of all partial maps on Xn={1,2,…,n}, and show that the classical decomposition of permutations into disjoint cycles can be extended to elements of Pn by means of path-cycles. The device is used to obtain information about generating sets for the semigroup Pn\Sn, of all singular partial maps of Xn. Moreover, we give a definition for the (m,r)-rank of Pn\Sn and show that it is n(n+1)/2.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Generators and ranks in finite partial transformation semigroups
Article
published earlier
spellingShingle Generators and ranks in finite partial transformation semigroups
Garba, G.U.
Imam, A.T.
title Generators and ranks in finite partial transformation semigroups
title_full Generators and ranks in finite partial transformation semigroups
title_fullStr Generators and ranks in finite partial transformation semigroups
title_full_unstemmed Generators and ranks in finite partial transformation semigroups
title_short Generators and ranks in finite partial transformation semigroups
title_sort generators and ranks in finite partial transformation semigroups
url https://nasplib.isofts.kiev.ua/handle/123456789/156026
work_keys_str_mv AT garbagu generatorsandranksinfinitepartialtransformationsemigroups
AT imamat generatorsandranksinfinitepartialtransformationsemigroups