Combinatorial results for semigroups of order-preserving full transformations

A. Laradji, A. Umar

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Let On be the semigroup of all order-preserving full transformations of a finite chain, say Xn = {1, 2, ..., n}, and for a given full transformation α: Xn → Xn let f(α) = |{x Xn: xα = x}|. In this note we obtain and discuss formulae for f(n,r,k) = |{α → On: f(α) = r ∧ max(Im α) = k}| and J(n,r,k) = |{α → On: |Im α| = r ∧ max(Im α) = k}|. We also obtain similar results for E(On), the set of idempotents of On.

Original languageBritish English
Pages (from-to)51-62
Number of pages12
JournalSemigroup Forum
Issue number1
StatePublished - Feb 2006


  • Catalan number
  • Fibonacci number
  • Full transformation
  • Idempotent
  • Nilpotent
  • Order-decreasing
  • Order-preserving
  • Partial transformation
  • Semigroup


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