Sonlu zincir üzerindeki tam daralma dönüşümlerinin bazı alt yarıgruplarının rankları

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.

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

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,

PDF

___

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).