TY - JOUR
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 - http://www.scopus.com/inward/record.url?scp=80055077895&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80055077895&partnerID=8YFLogxK
U2 - 10.1142/S0218196711005954
DO - 10.1142/S0218196711005954
M3 - Article
AN - SCOPUS:80055077895
VL - 21
SP - 857
EP - 865
JO - International Journal of Algebra and Computation
JF - International Journal of Algebra and Computation
SN - 0218-1967
IS - 6
ER -