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

Year 2020, Volume: 22 Issue: 2, 403 - 414, 10.04.2020
https://doi.org/10.25092/baunfbed.707344

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.

Thanks

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

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).

Sonlu zincir üzerindeki tam daralma dönüşümlerinin bazı alt yarıgruplarının rankları

Year 2020, Volume: 22 Issue: 2, 403 - 414, 10.04.2020
https://doi.org/10.25092/baunfbed.707344

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.

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).
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Details

Primary Language English
Journal Section Research Articles
Authors

Kemal Toker 0000-0003-3696-1324

Publication Date April 10, 2020
Submission Date September 28, 2019
Published in Issue Year 2020 Volume: 22 Issue: 2

Cite

APA Toker, K. (2020). Ranks of some subsemigroups of full contraction mappings on a finite chain. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(2), 403-414. https://doi.org/10.25092/baunfbed.707344
AMA Toker K. Ranks of some subsemigroups of full contraction mappings on a finite chain. BAUN Fen. Bil. Enst. Dergisi. April 2020;22(2):403-414. doi:10.25092/baunfbed.707344
Chicago Toker, Kemal. “Ranks of Some Subsemigroups of Full Contraction Mappings on a Finite Chain”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, no. 2 (April 2020): 403-14. https://doi.org/10.25092/baunfbed.707344.
EndNote Toker K (April 1, 2020) Ranks of some subsemigroups of full contraction mappings on a finite chain. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 2 403–414.
IEEE K. Toker, “Ranks of some subsemigroups of full contraction mappings on a finite chain”, BAUN Fen. Bil. Enst. Dergisi, vol. 22, no. 2, pp. 403–414, 2020, doi: 10.25092/baunfbed.707344.
ISNAD Toker, Kemal. “Ranks of Some Subsemigroups of Full Contraction Mappings on a Finite Chain”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/2 (April 2020), 403-414. https://doi.org/10.25092/baunfbed.707344.
JAMA Toker K. Ranks of some subsemigroups of full contraction mappings on a finite chain. BAUN Fen. Bil. Enst. Dergisi. 2020;22:403–414.
MLA Toker, Kemal. “Ranks of Some Subsemigroups of Full Contraction Mappings on a Finite Chain”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, no. 2, 2020, pp. 403-14, doi:10.25092/baunfbed.707344.
Vancouver Toker K. Ranks of some subsemigroups of full contraction mappings on a finite chain. BAUN Fen. Bil. Enst. Dergisi. 2020;22(2):403-14.