# Some combinatorial properties of the symmetric monoid

Research output: Contribution to journalArticle

2 Citations (Scopus)

### 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 857-865 9 International Journal of Algebra and Computation 21 6 https://doi.org/10.1142/S0218196711005954 Published - Sep 2011

### Fingerprint

Transformation Semigroups
Monoid
Finite Set
Fixed point

### Keywords

• Green's equivalences
• idempotents
• semigroups
• transformations

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

Some combinatorial properties of the symmetric monoid. / Laradji, A.; Umar, A.

In: International Journal of Algebra and Computation, Vol. 21, No. 6, 09.2011, p. 857-865.

Research output: Contribution to journalArticle

Laradji, A. ; Umar, A. / Some combinatorial properties of the symmetric monoid. In: International Journal of Algebra and Computation. 2011 ; Vol. 21, No. 6. pp. 857-865.
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