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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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2017 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2017
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/156026 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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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nasplib_isofts_kiev_ua-123456789-156026 |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Generators and ranks in finite partial transformation semigroups |
| spellingShingle |
Generators and ranks in finite partial transformation semigroups Garba, G.U. Imam, A.T. |
| title_short |
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_sort |
generators and ranks in finite partial transformation semigroups |
| author |
Garba, G.U. Imam, A.T. |
| author_facet |
Garba, G.U. Imam, A.T. |
| publishDate |
2017 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/156026 |
| 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. |
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AT garbagu generatorsandranksinfinitepartialtransformationsemigroups AT imamat generatorsandranksinfinitepartialtransformationsemigroups |
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2025-12-01T13:59:30Z |
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2025-12-01T13:59:30Z |
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1850860357957976064 |