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Combinatorial results for semigroups of order-preserving mappings

Published online by Cambridge University Press:  24 October 2008

Peter M. Higgins
Peter M. Higgins
Affiliation:
Department of Mathematics, University of Essex
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Extract

Consider the finite set Xn = {1,2, …,n} ordered in the standard way. Let Tn denote the full transformation semigroup on Xn, that is, the semigroup of all mappings α: Xn→Xn under composition. We shall call α order-preserving if i ≤ j implies iα ≤ jα for i,j∈Xn, and α is decreasing if iα ≤ i for all i∈Xn. This paper investigates combinatorial properties of the semigroup O of all order-preserving mappings on Xn, and of its subsemigroup C which consists of all decreasing and order-preserving mappings.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 2 , March 1993 , pp. 281 - 296
Copyright
Copyright © Cambridge Philosophical Society 1993

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