Some combinatorial problems in the theory of partial transformation semigroups

• Date: 2018
• Main Author: Umar, A.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: full transformation; partial transformation; breadth; collapse; fix; height and right (left) waist of a transformation. Idempotents and nilpotents; 20M17; 20M20; 05A10; 05A15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1027
• Journal Title: Algebra and Discrete Mathematics

Let \(X_n = \{1, 2, \ldots , n\}\). On a partial transformation \(\alpha : \mathop{\rm Dom}\nolimits \alpha \subseteq  X_n \rightarrow \mbox{Im}\,\alpha \subseteq X_n\) of \(X_n\) the following parameters are defined: the  breadth  or  width of \(\alpha\) is \(\mid{\mathop{\rm Dom}\nolimits}\  \alph...