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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив |
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RESEARCH ARTICLE
Some combinatorial problems in the theory of symmetric inverse semigroups
A. Umar
Department of Mathematics and Statistics Sultan Qaboos University, Al-Khod, PC 123 – OMAN
Аннотация: Let$X_n =\{1, 2,\cdots,n\}$ and let $\alpha:\operatorname{Dom}\alpha\subseteq X_n\rightarrow\operatorname{Im}\alpha\subseteq X_n$ be a (partial) transformation on $X_n$ . On a partial one-one mapping of $X_n$ the following parameters are defined: the height of $\alpha$ is $h(\alpha)=|\operatorname{Im}\alpha|$ , the right [left] waist of $\alpha$ is $w^+(\alpha)=\max(\operatorname{Im}\alpha)[w^-(\alpha)=\min(\operatorname{Im}\alpha)]$, and fix of $\alpha$ is denoted by $f(\alpha)$ , and defined by $f(\alpha)=|\{x\in X_n:x\alpha=x\}|$ . The cardinalities of some equivalences defined by equalities of these parameters on ${\mathcal I}_n$ , the semigroup of partial one-one mappings of $X_n$ , and some of its notable subsemigroups that have been computed are gathered together and the open problems highlighted.
Ключевые слова: partial one-one transformation, height, right (left) waist and fix of a transformation. Idempotents and nilpotents.
MSC: 20M18, 20M20, 05A10, 05A15
Поступила в редакцию: 19.08.2010
Исправленный вариант: 11.11.2010
Язык публикации: английский
RESEARCH ARTICLE
Some combinatorial problems in the theory of symmetric inverse semigroups
A. Umar
Department of Mathematics and Statistics Sultan Qaboos University, Al-Khod, PC 123 – OMAN
Аннотация: Let
Ключевые слова: partial one-one transformation, height, right (left) waist and fix of a transformation. Idempotents and nilpotents.
MSC: 20M18, 20M20, 05A10, 05A15
Поступила в редакцию: 19.08.2010
Исправленный вариант: 11.11.2010
Язык публикации: английский