Combinatorial results for semigroups of order-decreasing partial transformations

A. Laradji, A. Umar

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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 languageBritish English
JournalJournal of Integer Sequences
Issue number3
StatePublished - 2004


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


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