On the large rank of certain semigroups of transformations on a finite chain

Abstract

The large rank of a finite semigroup S is the least number n such that every subset of S with n elements generates S. This paper obtains the large ranks of ODn,PODJn and PODn, the semigroups of singular transformations, injective partial and partial transformations on a finite chain [n]={1,2,…,n}, which preserve or reverse the order, respectively. As a consequence, we obtain the large ranks of POJn and POn, the semigroups of injective order-preserving partial transformations and order-preserving partial transformations on [n], respectively.