Abstract
Let Tnbe the full transformation semigroup of a finite set, say Xn= {1, 2, …, n}, and for a given full transformation α : Xn→ Xnlet 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}|.
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