Generators and ranks in finite partial transformation semigroups

• Date: 2017
• Main Authors: Garba, Goje Uba, Imam, Abdussamad Tanko
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2017
• Subjects: path-cycle; (\(m,r\))-path-cycle; \(m\)-path; generating set; (\(m,r\))-rank; 20M20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/128
• Journal Title: Algebra and Discrete Mathematics

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...