Enumeration of certain finite semigroups of transformations

Abdullahi Umar

doi:10.1016/S0012-365X(94)00357-O

Enumeration of certain finite semigroups of transformations

Abdullahi Umar^*

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

Let Sing_n be the semigroup of singular self-maps of X_n = {1, ... ,n}, let R_n = {α ∈ Sing_n: (∀y ∈ Im α)|yα^-1| ≥ |Im α|} and let E(R_n) be the set of idempotents of R_n. Then it is shown that R_n = (E(R_n))². Moreover, expressions for the order of R_n and E(R_n) 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 X_n into r subsets each of size not less than k.

Original language	English
Pages (from-to)	291-297
Number of pages	7
Journal	Discrete Mathematics
Volume	189
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(94)00357-O
Publication status	Published - Jul 28 1998
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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

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title = "Enumeration of certain finite semigroups of transformations",

abstract = "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.",

author = "Abdullahi Umar",

note = "Funding Information: Financial support from the Federal Government of Nigeria is gratefully acknowledged.",

year = "1998",

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doi = "10.1016/S0012-365X(94)00357-O",

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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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JO - Discrete Mathematics

JF - Discrete Mathematics

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ER -

Enumeration of certain finite semigroups of transformations

Abstract

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