(Combinatorial Press, 2018-06-01) A. D. Adeshola and A. Umar
Let Tn be the full symmetric semigroup on Xn = f1; 2; : : : ; ng
and let OCT n and ORCT n be its subsemigroups of order-preserving
and order-preserving or order-reversing full contraction mappings of
Xn, respectively. In this paper we investigate the cardinalities of
some equivalences on OCT n and ORCT n which lead naturally to
obtaining the orders of these subsemigroups. 1, 2,