Ali , B., M. A. Jada, and M. M. Zubairu. “On Rank of Semigroup of Order-Preserving Order-Decreasing Partial Contraction Mappings on a Finite Chain”. International Journal of Mathematical Sciences and Optimization: Theory and Applications, Vol. 10, no. 4, Sept. 2024, pp. 1 - 11, http://ijmso.unilag.edu.ng/article/view/2384.