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...
Збережено в:
| 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| Резюме: | 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. |
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