Some combinatorial problems in the theory of symmetric inverse semigroups

• Date: 2018
• Main Author: Umar, A.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: partial one-one transformation; height; right (left) waist and fix of a transformation. Idempotents and nilpotents; 20M18; 20M20; 05A10; 05A15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/635
• Journal Title: Algebra and Discrete Mathematics

Let \(X_n = \{1, 2, \cdots , n\}\) and let \(\alpha : \mathop{\rm Dom}\nolimits \alpha \subseteq  X_n \rightarrow \mathop{\rm Im}\nolimits \alpha \subseteq X_n\) be a (partial) transformation on \(X_n\). On a partial one-one mapping of \(X_n\) the following parameters are defined: the height of \(\a...