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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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2017
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1560262019-06-18T01:30:53Z Generators and ranks in finite partial transformation semigroups Garba, G.U. Imam, A.T. 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. 2017 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/156026 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Garba, G.U. Imam, A.T. |
| spellingShingle |
Garba, G.U. Imam, A.T. Generators and ranks in finite partial transformation semigroups Algebra and Discrete Mathematics |
| author_facet |
Garba, G.U. Imam, A.T. |
| author_sort |
Garba, G.U. |
| title |
Generators and ranks in finite partial transformation semigroups |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT garbagu generatorsandranksinfinitepartialtransformationsemigroups AT imamat generatorsandranksinfinitepartialtransformationsemigroups |
| first_indexed |
2023-05-20T17:48:43Z |
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2023-05-20T17:48:43Z |
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1796154144976797696 |