Kemal TOKER

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,

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