1. Catarino, P.M.: Monoids of orientation-preserving transformations of a finite chain and their representations. In: Howie, John M., Ruskuc, Nik (eds.) Proceedings of the Conference on Semigroups and Applications, pp. 39–46. World Scientific, St. Andrews (1997)
2. Catarino, P.M., Higgins, P.M.: The Monoid of orientation-preserving Mappings on a chain. Semigroup Forum 58, 190–206 (1999)
3. Clifford, H., Preston, G.B.: The Algebraic Theory of Semigroups, 1. Am. Math. Soc, Providence (1961)
4. Fernandes, V.H.: The monoid of all injective order-preserving partial transformations on a finite chain. Semigroup Forum 62, 178–204 (2001)
5. Garba, G.U.: On the idempotent ranks of certain semigroups of order-preserving transformations. Port. Math. 51(2), 185–204 (1994)