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

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

3 Scopus citations

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
State	Published - Sep 2011

Bibliographical note

Funding Information:
The authors would like to gratefully acknowledge support from the King Fahd University of Petroleum and Minerals and Sultan Qaboos University.

Keywords

Green's equivalences
idempotents
semigroups
transformations

ASJC Scopus subject areas

General Mathematics

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10.1142/S0218196711005954

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title = "Some combinatorial properties of the symmetric monoid",

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\}|.",

keywords = "Green's equivalences, idempotents, semigroups, transformations",

author = "A. Laradji and A. Umar",

note = "Funding Information: The authors would like to gratefully acknowledge support from the King Fahd University of Petroleum and Minerals and Sultan Qaboos University.",

year = "2011",

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T1 - Some combinatorial properties of the symmetric monoid

AU - Laradji, A.

AU - Umar, A.

N1 - Funding Information: The authors would like to gratefully acknowledge support from the King Fahd University of Petroleum and Minerals and Sultan Qaboos University.

PY - 2011/9

Y1 - 2011/9

N2 - 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}|.

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}|.

KW - Green's equivalences

KW - idempotents

KW - semigroups

KW - transformations

UR - https://www.scopus.com/pages/publications/80055077895

U2 - 10.1142/S0218196711005954

DO - 10.1142/S0218196711005954

M3 - Article

AN - SCOPUS:80055077895

SN - 0218-1967

VL - 21

SP - 857

EP - 865

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 6

ER -

Some combinatorial properties of the symmetric monoid

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this