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.
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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 -