Ahmed, B. M. and Makanjuola, S. O.2025-05-082025-05-082016Ahmed, B. M. and Makanjuola, S. O. (2016): Combinatorial Properties of Order-Preserving and Order – Decreasing Semigroup of Partial Injective Contraction Mapping, Nigerian Journal of Mathematics and Applications, 25, 65 – 79. Published by Mathematical Association of Nigeria.https://uilspace.unilorin.edu.ng/handle/123456789/16453Let CI_n be the semigroup of partial injective contraction mappings. The focus of this paper is to provide some properties subsemigroups of CI_n which are semigroup of order preserving partial injective contraction mapping (OCI_n) and semigroup of order decreasing partial injective contraction mapping (DCI_n). The results on this work are combinatorial properties of subsemigroups of CI_n which are both order preserving and other decreasing denoted by ODCI_n.en