TY - JOUR

T1 - Enumeration of certain finite semigroups of transformations

AU - Umar, Abdullahi

N1 - Funding Information:
Financial support from the Federal Government of Nigeria is gratefully acknowledged.

PY - 1998/7/28

Y1 - 1998/7/28

N2 - Let Singn be the semigroup of singular self-maps of Xn = {1, ... ,n}, let Rn = {α ∈ Singn: (∀y ∈ Im α)|yα-1| ≥ |Im α|} and let E(Rn) be the set of idempotents of Rn. Then it is shown that Rn = (E(Rn))2. Moreover, expressions for the order of Rn and E(Rn) are obtained in terms of the kth-upper Stirling number of the second kind, S(n,r,k); defined as the number of partitions of Xn into r subsets each of size not less than k.

AB - Let Singn be the semigroup of singular self-maps of Xn = {1, ... ,n}, let Rn = {α ∈ Singn: (∀y ∈ Im α)|yα-1| ≥ |Im α|} and let E(Rn) be the set of idempotents of Rn. Then it is shown that Rn = (E(Rn))2. Moreover, expressions for the order of Rn and E(Rn) are obtained in terms of the kth-upper Stirling number of the second kind, S(n,r,k); defined as the number of partitions of Xn into r subsets each of size not less than k.

UR - http://www.scopus.com/inward/record.url?scp=0042284272&partnerID=8YFLogxK

U2 - 10.1016/S0012-365X(94)00357-O

DO - 10.1016/S0012-365X(94)00357-O

M3 - Article

AN - SCOPUS:0042284272

SN - 0012-365X

VL - 189

SP - 291

EP - 297

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -