### Abstract

Let script P sign script C sign n be the semigroup of all decreasing and order-preserving partial transformations of an n -element chain, and let E (script P sign script C sign n ) be its set of idempotents. Among other results, asymptotic formulae for |script P sign script C sign n | and | E (script P sign script C sign n )|/|script P sign script C sign n | are obtained. Similar results for script P sign script O sign n the (larger) semigroup of all order-preserving partial transformations of an n -element chain are also obtained.

Original language | English |
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Pages (from-to) | 1071-1075 |

Number of pages | 5 |

Journal | Communications in Algebra |

Volume | 34 |

Issue number | 3 |

DOIs | |

Publication status | Published - Feb 2006 |

### Keywords

- Double/small Schröder number
- Generating function
- Idempotents
- Integral representation
- Legendre polynomial
- Order-decreasing/order-preserving partial transformations
- Semigroup
- Stirling's formula

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Laradji, A., & Umar, A. (2006). Asymptotic results for semigroups of order-preserving partial transformations.

*Communications in Algebra*,*34*(3), 1071-1075. https://doi.org/10.1080/00927870500442039