Enumeration of certain finite semigroups of transformations

Abdullahi Umar

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)291-297
Number of pages7
JournalDiscrete Mathematics
Volume189
Issue number1-3
Publication statusPublished - Jul 28 1998

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Stirling numbers of the second kind
Idempotent
Enumeration
Semigroup
Partition
Subset

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Enumeration of certain finite semigroups of transformations. / Umar, Abdullahi.

In: Discrete Mathematics, Vol. 189, No. 1-3, 28.07.1998, p. 291-297.

Research output: Contribution to journalArticle

Umar, Abdullahi. / Enumeration of certain finite semigroups of transformations. In: Discrete Mathematics. 1998 ; Vol. 189, No. 1-3. pp. 291-297.
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