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

Year 2020, Volume: 22 Issue: 2, 403 - 414, 10.04.2020

Kemal Toker

https://doi.org/10.25092/baunfbed.707344

Cited By: 1

Abstract

Let Z^+denotes the set of all positive integers. Let X_n={1,2,…,n} be the finite chain for n∈Z^+ and let T_n be the full transformation semigroup on X_n. 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.

Keywords

Order-preserving/order-reversing contraction mappings, generating set

Thanks

We would like to thank the referees for their valuable comments which helped to improve the manuscript.

Sonlu zincir üzerindeki tam daralma dönüşümlerinin bazı alt yarıgruplarının rankları

Abstract

Z^+, tüm pozitif tamsayıların kümesi olsun. n∈Z^+ için X_n={1,2,…,n} sonlu bir zincir ve T_n, X_n üzerindeki tam dönüşümler yarıgrubu olsun. Ayrıca 〖OCT〗_n ve 〖ORCT〗_n sırasıyla X_n üzerindeki sıra-koruyan tam daralma dönüşümler yarıgrubu ve sıra-koruyan veya sıra-çeviren tam daralma dönüşüler yarıgrubu olsun.〖OCT〗_n ve 〖ORCT〗_n yarıgruplarının T_n yarıgrubunun altyarıgrupları olduğu bilinmektedir. Bu çalışmada 〖OCT〗_n ve 〖ORCT〗_n yarıgruplarının rankları araştırılmıştır.

Keywords

Sıra-koruyan/sıra-çeviren daralma dönüşümleri, doğuray kümeleri

References

• 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, 101, 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).