Combinatorial results for semigroups of order-preserving partial transformations

A. Laradji; A. Umar

doi:10.1016/j.jalgebra.2003.10.023

Combinatorial results for semigroups of order-preserving partial transformations

A. Laradji, A. Umar^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

Abstract

Let PO_n be the semigroup of all order-preserving partial transformations of a finite chain. It is shown that PO_n =c_n satisfies the recurrence (2n-1)(n+1)c_n+1=4 (3n²-1 c_n-(2n+1) (n-1)c_n-1 with initial conditions c₀=1, c₁=2. It is also shown that E(PO_n) =e_n satisfies the recurrence e_n+1=5(e_n-e_n-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
Pages (from-to)	342-359
Number of pages	18
Journal	Journal of Algebra
Volume	278
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2003.10.023
Publication status	Published - Aug 1 2004
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2003.10.023

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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",

note = "Funding Information: We gratefully acknowledge support from the King Fahd University of Petroleum and Minerals. We also thank the referee for providing useful suggestions.",

year = "2004",

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AU - Laradji, A.

AU - Umar, A.

N1 - Funding Information: We gratefully acknowledge support from the King Fahd University of Petroleum and Minerals. We also thank the referee for providing useful suggestions.

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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Combinatorial results for semigroups of order-preserving partial transformations

Abstract

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