Combinatorial results for semigroups of order-decreasing partial transformations

A. Laradji; A. Umar

Combinatorial results for semigroups of order-decreasing partial transformations

A. Laradji^*, A. Umar

^*Corresponding author for this work

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

13 Citations (Scopus)

Abstract

Let PC_n be the semigroup of all decreasing and order-preserving partial transformations of a finite chain. It is shown that |PC_n| = r_n, where r_n is the large (or double) Schröder number. Moreover, the total number of idempotents of PC_n is shown to be (3ⁿ +1)/2.

Original language	English
Journal	Journal of Integer Sequences
Volume	7
Issue number	3
Publication status	Published - 2004
Externally published	Yes

Keywords

Catalan number
Fibonacci number
Full transformation
Narayana numbers
Order-decreasing
Order-preserving
Partial transformation
Schröder numbers
Semigroup

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Cite this

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title = "Combinatorial results for semigroups of order-decreasing partial transformations",

abstract = "Let PCn be the semigroup of all decreasing and order-preserving partial transformations of a finite chain. It is shown that |PCn| = rn, where rn is the large (or double) Schr{\"o}der number. Moreover, the total number of idempotents of PCn is shown to be (3n +1)/2.",

keywords = "Catalan number, Fibonacci number, Full transformation, Narayana numbers, Order-decreasing, Order-preserving, Partial transformation, Schr{\"o}der numbers, Semigroup",

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

year = "2004",

language = "English",

volume = "7",

journal = "Journal of Integer Sequences",

issn = "1530-7638",

publisher = "University of Waterloo",

number = "3",

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TY - JOUR

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

AU - Laradji, A.

AU - Umar, A.

PY - 2004

Y1 - 2004

N2 - Let PCn be the semigroup of all decreasing and order-preserving partial transformations of a finite chain. It is shown that |PCn| = rn, where rn is the large (or double) Schröder number. Moreover, the total number of idempotents of PCn is shown to be (3n +1)/2.

AB - Let PCn be the semigroup of all decreasing and order-preserving partial transformations of a finite chain. It is shown that |PCn| = rn, where rn is the large (or double) Schröder number. Moreover, the total number of idempotents of PCn is shown to be (3n +1)/2.

KW - Catalan number

KW - Fibonacci number

KW - Full transformation

KW - Narayana numbers

KW - Order-decreasing

KW - Order-preserving

KW - Partial transformation

KW - Schröder numbers

KW - Semigroup

UR - http://www.scopus.com/inward/record.url?scp=11844258206&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11844258206&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:11844258206

SN - 1530-7638

VL - 7

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

IS - 3

ER -

Combinatorial results for semigroups of order-decreasing partial transformations

Abstract

Keywords

ASJC Scopus subject areas

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