Asymptotic results for semigroups of order-preserving partial transformations

A. Laradji; A. Umar

doi:10.1080/00927870500442039

Asymptotic results for semigroups of order-preserving partial transformations

A. Laradji, A. Umar

Mathematics

King Fahd University for Petroleum and Minerals (KFUPM)

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

3 Scopus citations

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	British English
Pages (from-to)	1071-1075
Number of pages	5
Journal	Communications in Algebra
Volume	34
Issue number	3
DOIs	https://doi.org/10.1080/00927870500442039
State	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

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10.1080/00927870500442039

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title = "Asymptotic results for semigroups of order-preserving partial transformations",

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.",

keywords = "Double/small Schr{\"o}der number, Generating function, Idempotents, Integral representation, Legendre polynomial, Order-decreasing/order-preserving partial transformations, Semigroup, Stirling's formula",

author = "A. Laradji and A. Umar",

note = "Funding Information: We would like to gratefully acknowledge the support from the King Fahd University of Petroleum and Minerals.",

year = "2006",

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doi = "10.1080/00927870500442039",

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pages = "1071--1075",

journal = "Communications in Algebra",

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TY - JOUR

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

AU - Laradji, A.

AU - Umar, A.

N1 - Funding Information: We would like to gratefully acknowledge the support from the King Fahd University of Petroleum and Minerals.

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

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U2 - 10.1080/00927870500442039

DO - 10.1080/00927870500442039

M3 - Article

AN - SCOPUS:33645067385

SN - 0092-7872

VL - 34

SP - 1071

EP - 1075

JO - Communications in Algebra

JF - Communications in Algebra

IS - 3

ER -

Asymptotic results for semigroups of order-preserving partial transformations

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Keywords

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