Asymptotic results for semigroups of order-preserving partial transformations

A. Laradji, A. Umar

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)1071-1075
Number of pages5
JournalCommunications in Algebra
Volume34
Issue number3
DOIs
Publication statusPublished - Feb 2006

    Fingerprint

Keywords

  • Double/small Schröder number
  • Generating function
  • Idempotents
  • Integral representation
  • Legendre polynomial
  • Order-decreasing/order-preserving partial transformations
  • Semigroup
  • Stirling's formula

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this