### 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 |

### Fingerprint

### 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

### Cite this

*Communications in Algebra*,

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

**Asymptotic results for semigroups of order-preserving partial transformations.** / Laradji, A.; Umar, A.

Research output: Contribution to journal › Article

*Communications in Algebra*, vol. 34, no. 3, pp. 1071-1075. https://doi.org/10.1080/00927870500442039

}

TY - JOUR

T1 - Asymptotic results for semigroups of order-preserving partial transformations

AU - Laradji, A.

AU - Umar, A.

PY - 2006/2

Y1 - 2006/2

N2 - 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.

AB - 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.

KW - Double/small Schröder number

KW - Generating function

KW - Idempotents

KW - Integral representation

KW - Legendre polynomial

KW - Order-decreasing/order-preserving partial transformations

KW - Semigroup

KW - Stirling's formula

UR - http://www.scopus.com/inward/record.url?scp=33645067385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645067385&partnerID=8YFLogxK

U2 - 10.1080/00927870500442039

DO - 10.1080/00927870500442039

M3 - Article

VL - 34

SP - 1071

EP - 1075

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 3

ER -