Combinatorial results for certain semigroups of partial isometries of a finite chain
F. Al-Kharousi, Rotimi Kehinde, Abdullahi Umar · 2014
Let In be the symmetric inverse semigroup on Xn = {1, 2 ,...,n } under composition of maps and let DPn and ODPn be its subsemigroups of partial isometries and of order-preserving partial isometries of Xn, respectively. In this paper we investigate the cardinalities of some equivalences on DPn and ODPn which lead naturally to obtaining the orders of these semigroups.