Ranks of some subsemigroups of full contraction mappings on a finite chain

Kemal Toker

Öz


Let Z^+ denotes the set of all positive integers. Let X_n={1,2,...,n} be the finite chain for n \in Z^+ and let T_n be the full transformation semigroup on . Also let OCT_n and ORCT_n  be the semigroup of order-preserving full contraction mappings, and the semigroup of order-preserving or order-reversing full contraction mappings on X_n, respectively. It is well-known that  OCT_n and  ORCT_n are subsemigroups of T_n. In this paper we obtain ranks of the semigroups OCT_n and ORCT_n.

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Referanslar


Garba, G.U., Ibrahim, M.J. and Imam, A.T., On certain semigroups of full contraction maps of a finite chain, Turkish Journal of Mathematics, 41, 3, 500-507, (2017).

Adeshola, A.D. and Umar, A., Results for certain semigroups of order-preserving full contraction mappings of a finite chain, Journal of Combinatorial Mathematics and Combinatorial Computing, 106, 37-49, (2018).

Gomes, G.M.S. and Howie, J.M., On the ranks of certain finite semigroups of transformations, Mathematical Proceedings of the Cambridge Philosophical Society,

, 3, 395-403, (1987).

Ayık, G., Ayık, H., Bugay, L. and Kelekci, O., Generating sets of finite singular transformation semigroups, Semigroup Forum, 86, 1, 59-66, (2013).

Bugay, L., Yağcı, M. And Ayık, H., The ranks of certain semigroups of partial isometries, Semigroup Forum, 97, 2, 214-222, (2018).

Toker, K. and Ayık, H., On the rank of transformation semigroup T_((n,m)), Turkish Journal of Mathematics, 42, 4, 1970-1977, (2018).

Howie, J.M., Fundamentals of Semigroup Theory, Oxford University Press, USA, (1995).


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