Generators and ranks in finite partial transformation semigroups
We extend the concept of path-cycle, to the semigroup \(\mathcal{P}_{n}\), of all partial maps on \(X_{n}=\{1,2,\ldots,n\}\), and show that the classical decomposition of permutations into disjoint cycles can be extended to elements of \(\mathcal{P}_{n}\) by means of path-cycles. The device is used...
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| Date: | 2017 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2017
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/128 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543290603601920 |
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| author | Garba, Goje Uba Imam, Abdussamad Tanko |
| author_facet | Garba, Goje Uba Imam, Abdussamad Tanko |
| author_sort | Garba, Goje Uba |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2017-07-02T21:58:40Z |
| description | We extend the concept of path-cycle, to the semigroup \(\mathcal{P}_{n}\), of all partial maps on \(X_{n}=\{1,2,\ldots,n\}\), and show that the classical decomposition of permutations into disjoint cycles can be extended to elements of \(\mathcal{P}_{n}\) by means of path-cycles. The device is used to obtain information about generating sets for the semigroup \(\mathcal{P}_{n}\setminus\mathcal{S}_{n}\), of all singular partial maps of \(X_{n}\). Moreover, we give a definition for the (\(m,r\))-rank of \(\mathcal{P}_{n}\setminus\mathcal{S}_{n}\) and show that it is \(\frac{n(n+1)}{2}\). |
| first_indexed | 2025-12-02T15:25:17Z |
| format | Article |
| id | admjournalluguniveduua-article-128 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:25:17Z |
| publishDate | 2017 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-1282017-07-02T21:58:40Z Generators and ranks in finite partial transformation semigroups Garba, Goje Uba Imam, Abdussamad Tanko path-cycle, (\(m,r\))-path-cycle, \(m\)-path, generating set, (\(m,r\))-rank 20M20 We extend the concept of path-cycle, to the semigroup \(\mathcal{P}_{n}\), of all partial maps on \(X_{n}=\{1,2,\ldots,n\}\), and show that the classical decomposition of permutations into disjoint cycles can be extended to elements of \(\mathcal{P}_{n}\) by means of path-cycles. The device is used to obtain information about generating sets for the semigroup \(\mathcal{P}_{n}\setminus\mathcal{S}_{n}\), of all singular partial maps of \(X_{n}\). Moreover, we give a definition for the (\(m,r\))-rank of \(\mathcal{P}_{n}\setminus\mathcal{S}_{n}\) and show that it is \(\frac{n(n+1)}{2}\). Lugansk National Taras Shevchenko University 2017-07-03 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/128 Algebra and Discrete Mathematics; Vol 23, No 2 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/128/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/128/212 Copyright (c) 2017 Algebra and Discrete Mathematics |
| spellingShingle | path-cycle (\(m,r\))-path-cycle \(m\)-path generating set (\(m,r\))-rank 20M20 Garba, Goje Uba Imam, Abdussamad Tanko Generators and ranks in finite partial transformation semigroups |
| 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 |
| topic | path-cycle (\(m,r\))-path-cycle \(m\)-path generating set (\(m,r\))-rank 20M20 |
| topic_facet | path-cycle (\(m,r\))-path-cycle \(m\)-path generating set (\(m,r\))-rank 20M20 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/128 |
| work_keys_str_mv | AT garbagojeuba generatorsandranksinfinitepartialtransformationsemigroups AT imamabdussamadtanko generatorsandranksinfinitepartialtransformationsemigroups |