Some combinatorial properties of the symmetric monoid

A. Laradji; A. Umar

doi:10.1142/S0218196711005954

Some combinatorial properties of the symmetric monoid

A. Laradji^*, A. Umar

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let T_n be the full transformation semigroup of a finite set, say X_n = {1, 2, ..., n}, and for a given full transformation α : X_n → X_n let F(α) = {x ∈ X_n : xα = x} be its set of fixed points. In this note we obtain and discuss formulae for F(n, r, k) = |{α ∈ T_n : |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	https://doi.org/10.1142/S0218196711005954
Publication status	Published - Sep 2011

Keywords

Green's equivalences
idempotents
semigroups
transformations

ASJC Scopus subject areas

Mathematics(all)

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10.1142/S0218196711005954

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AB - 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}|.

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KW - idempotents

KW - semigroups

KW - transformations

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