Some combinatorial properties of the symmetric monoid

A. Laradji, A. Umar

Research output: Contribution to journal › Article

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 languageEnglish
Pages (from-to)857-865
Number of pages9
JournalInternational Journal of Algebra and Computation
Volume21
Issue number6
DOIs
Publication statusPublished - Sep 2011

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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 journal › Article

Laradji, A & Umar, A 2011, 'Some combinatorial properties of the symmetric monoid', International Journal of Algebra and Computation, vol. 21, no. 6, pp. 857-865. https://doi.org/10.1142/S0218196711005954
Laradji A, Umar A. Some combinatorial properties of the symmetric monoid. International Journal of Algebra and Computation. 2011 Sep;21(6):857-865. https://doi.org/10.1142/S0218196711005954
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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