Some combinatorial properties of the symmetric monoid

A. Laradji*, A. Umar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Let Tn be the full transformation semigroup of a finite set, say Xn = {1, 2, ..., n}, and for a given full transformation α : Xn → Xn let F(α) = {x ∈ Xn : xα = x} be its set of fixed points. In this note we obtain and discuss formulae for F(n, r, k) = |{α ∈ Tn : |Im α| = r ∧ |F(α)| = k}|.

Original languageEnglish
Pages (from-to)857-865
Number of pages9
JournalInternational Journal of Algebra and Computation
Issue number6
Publication statusPublished - Sept 2011


  • Green's equivalences
  • idempotents
  • semigroups
  • transformations

ASJC Scopus subject areas

  • Mathematics(all)


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