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...
Gespeichert in:
| Datum: | 2017 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2017
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/128 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-128 |
|---|---|
| record_format |
ojs |
| spelling |
oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2017-07-02T21:58:40Z |
| collection |
OJS |
| language |
English |
| topic |
path-cycle (\(m,r\))-path-cycle \(m\)-path generating set (\(m,r\))-rank 20M20 |
| 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 |
| topic_facet |
path-cycle (\(m,r\))-path-cycle \(m\)-path generating set (\(m,r\))-rank 20M20 |
| format |
Article |
| author |
Garba, Goje Uba Imam, Abdussamad Tanko |
| author_facet |
Garba, Goje Uba Imam, Abdussamad Tanko |
| author_sort |
Garba, Goje Uba |
| 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 |
| 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 \(\frac{n(n+1)}{2}\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2017 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/128 |
| work_keys_str_mv |
AT garbagojeuba generatorsandranksinfinitepartialtransformationsemigroups AT imamabdussamadtanko generatorsandranksinfinitepartialtransformationsemigroups |
| first_indexed |
2025-07-17T10:30:02Z |
| last_indexed |
2025-07-17T10:30:02Z |
| _version_ |
1837889817770196992 |