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

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

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