Combinatorial results for the symmetric inverse semigroup

A. Laradji, A. Umar

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this note we obtain and discuss formulae for the number of partial one-one transformations (of an n-element set) of height (equivalently, width) r and having exactly k fixed points. Moreover, we consider a generalization of the 'Hat Problem' or 'Probleme des Rencontres'.

Original languageBritish English
Pages (from-to)221-236
Number of pages16
JournalSemigroup Forum
Issue number1
StatePublished - Sep 2007


  • Derangement
  • Exponential generating function
  • Full transformation
  • Laguerre polynomial
  • Nilpotent
  • Ordinary generating function
  • Partial one-one transformation
  • Partial transformation
  • Permutation
  • Semigroup


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