### Abstract

Let Sing_{n} be the semigroup of singular self-maps of X_{n} = {1, ... ,n}, let R_{n} = {α ∈ Sing_{n}: (∀y ∈ Im α)|yα^{-1}| ≥ |Im α|} and let E(R_{n}) be the set of idempotents of R_{n}. Then it is shown that R_{n} = (E(R_{n}))^{2}. Moreover, expressions for the order of R_{n} and E(R_{n}) are obtained in terms of the kth-upper Stirling number of the second kind, S(n,r,k); defined as the number of partitions of X_{n} into r subsets each of size not less than k.

Original language | English |
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Pages (from-to) | 291-297 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 189 |

Issue number | 1-3 |

Publication status | Published - Jul 28 1998 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

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## Cite this

Umar, A. (1998). Enumeration of certain finite semigroups of transformations.

*Discrete Mathematics*,*189*(1-3), 291-297.