A presentation for the semigroup of order-preserving full contraction mappings of a finite chain

For n is an element of Z+ , let Xn={1,& mldr;,n} be a finite chain and Tn be the full transformation semigroup on Xn . If OCTn is the set of all order-preserving and full contraction mappings on Xn , then it is well-known that OCTn is a submonoid of Tn . In this paper we give a monoid presentation of OCTn .