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...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2017
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/156026 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862647822715715584 |
|---|---|
| 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 |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156026 |
| 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 |