Abstract: | ABSTRACT In this paper we calculate presentations for some natural monoids of transformations on a chain X n = {1 < 2 s < n}. First we consider 𝒪𝒟 n [𝒫𝒪𝒟 n ], the monoid of all full [partial] transformations on X n that preserve or reverse the order. Two other monoids of partial transformations on X n we look at are 𝒫𝒪𝒫 n and 𝒫𝒪? n –-the elements of the first preserve the orientation and the elements of the second preserve or reverse the orientation. |