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On the semigroups of order-decreasing finite full transformations

Published online by Cambridge University Press:  14 November 2011

Abdullahi Umar
Abdullahi Umar
Affiliation:
Department of Mathematical Sciences, University of St Andrews, St Andrews KY16 9SS, Scotland, U.K.
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Synopsis

Let Singn be the subsemigroup of singular elements of the full transformation semigroup on a totally ordered finite set with n elements. Let be the subsemigroup of all decreasing maps of Singn. In this paper it is shown that is a non-regular abundant semigroup with n − 1 -classes and . Moreover, is idempotent-generated and it is generated by the n(n − 1)/2 idempotents in J*n−1. Let

and

Some recurrence relations satisfied by J*(n, r) and sh (n, r) are obtained. Further, it is shown that sh (n, r) is the complementary signless (or absolute) Stirling number of the first kind.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 1-2 , 1992 , pp. 129 - 142
Copyright
Copyright © Royal Society of Edinburgh 1992

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