Abstract
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 language | English |
|---|---|
| Pages (from-to) | 857-865 |
| Number of pages | 9 |
| Journal | International Journal of Algebra and Computation |
| Volume | 21 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - Sep 2011 |
Keywords
- Green's equivalences
- idempotents
- semigroups
- transformations
ASJC Scopus subject areas
- Mathematics(all)
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Cite this
Laradji, A., & Umar, A. (2011). Some combinatorial properties of the symmetric monoid. International Journal of Algebra and Computation, 21(6), 857-865. https://doi.org/10.1142/S0218196711005954