# Combinatorial results for semigroups of order-preserving partial transformations

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21 Citations (Scopus)

### Abstract

Let POn be the semigroup of all order-preserving partial transformations of a finite chain. It is shown that POn =cn satisfies the recurrence (2n-1)(n+1)cn+1=4 (3n2-1 cn-(2n+1) (n-1)cn-1 with initial conditions c0=1, c1=2. It is also shown that E(POn) =en satisfies the recurrence en+1=5(en-en-1)+1 with initial conditions e0=1, e1=2. Moreover, the cardinalities of the Green's relations L, R and J have been computed.

Original language English 342-359 18 Journal of Algebra 278 1 https://doi.org/10.1016/j.jalgebra.2003.10.023 Published - Aug 1 2004

### Fingerprint

Recurrence
Initial conditions
Semigroup
Green's Relations
Partial
Cardinality

### ASJC Scopus subject areas

• Algebra and Number Theory

### Cite this

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

In: Journal of Algebra, Vol. 278, No. 1, 01.08.2004, p. 342-359.

Research output: Contribution to journalArticle

Laradji, A. ; Umar, A. / Combinatorial results for semigroups of order-preserving partial transformations. In: Journal of Algebra. 2004 ; Vol. 278, No. 1. pp. 342-359.
title = "Combinatorial results for semigroups of order-preserving partial transformations",
abstract = "Let POn be the semigroup of all order-preserving partial transformations of a finite chain. It is shown that POn =cn satisfies the recurrence (2n-1)(n+1)cn+1=4 (3n2-1 cn-(2n+1) (n-1)cn-1 with initial conditions c0=1, c1=2. It is also shown that E(POn) =en satisfies the recurrence en+1=5(en-en-1)+1 with initial conditions e0=1, e1=2. Moreover, the cardinalities of the Green's relations L, R and J have been computed.",
author = "A. Laradji and A. Umar",
year = "2004",
month = "8",
day = "1",
doi = "10.1016/j.jalgebra.2003.10.023",
language = "English",
volume = "278",
pages = "342--359",
journal = "Journal of Algebra",
issn = "0021-8693",
number = "1",

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

AU - Umar, A.

PY - 2004/8/1

Y1 - 2004/8/1

N2 - Let POn be the semigroup of all order-preserving partial transformations of a finite chain. It is shown that POn =cn satisfies the recurrence (2n-1)(n+1)cn+1=4 (3n2-1 cn-(2n+1) (n-1)cn-1 with initial conditions c0=1, c1=2. It is also shown that E(POn) =en satisfies the recurrence en+1=5(en-en-1)+1 with initial conditions e0=1, e1=2. Moreover, the cardinalities of the Green's relations L, R and J have been computed.

AB - Let POn be the semigroup of all order-preserving partial transformations of a finite chain. It is shown that POn =cn satisfies the recurrence (2n-1)(n+1)cn+1=4 (3n2-1 cn-(2n+1) (n-1)cn-1 with initial conditions c0=1, c1=2. It is also shown that E(POn) =en satisfies the recurrence en+1=5(en-en-1)+1 with initial conditions e0=1, e1=2. Moreover, the cardinalities of the Green's relations L, R and J have been computed.

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U2 - 10.1016/j.jalgebra.2003.10.023

DO - 10.1016/j.jalgebra.2003.10.023

M3 - Article

AN - SCOPUS:3242661472

VL - 278

SP - 342

EP - 359

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -