Presentations for subsemigroups of $PD_n$
Abdullahi Umar · Czechoslovak Mathematical Journal · 2018
Let [n] = {1, . . ., n} be the n-chain.We give presentations for the following transformation semigroups: the semigroup of full order-decreasing mappings of [n], the semigroup of partial one-to-one order-decreasing mappings of [n], the semigroup of full order-preserving and order-decreasing mappings of [n], the semigroup of partial one-to-one order-preserving and order-decreasing mappings of [n], and the semigroup of partial order-preserving and orderdecreasing mappings of [n].