Combinatorial results for semigroups of order-decreasing partial transformations

A. Laradji, A. Umar

Research output: Contribution to journalArticle

11 Citations (Scopus)

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) Schröder number. Moreover, the total number of idempotents of PCn is shown to be (3n +1)/2.

Original languageEnglish
JournalJournal of Integer Sequences
Volume7
Issue number3
Publication statusPublished - 2004

Fingerprint

Semigroup
Partial
Idempotent

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

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

In: Journal of Integer Sequences, Vol. 7, No. 3, 2004.

Research output: Contribution to journalArticle

@article{2160c5bfaeb642d2a511a4fe2e3ef846,
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",

}

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

VL - 7

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

SN - 1530-7638

IS - 3

ER -