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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.

Поступила в редакцию: 19.08.2010
Исправленный вариант: 11.11.2010

Реферативные базы данных:

Образец цитирования: A. Umar, “Some combinatorial problems in the theory of symmetric inverse semigroups”, Algebra Discrete Math., 9:2 (2010), 115–126

Цитирование в формате AMSBIB

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https://www.mathnet.ru/rus/adm33

https://www.mathnet.ru/rus/adm/v9/i2/p115

Эта публикация цитируется в следующих 2 статьяx:

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