Idempotent rank in decreasing and order-preserving finite partial transformation semigroups
Huabi Hu · Journal of Shandong University · 2011
Let PCn be the semigroup of all decreasing and order-preserving partial transformations on [n].For n≥3,it is shown that the semigroup PCn is generated by idempotents of rank n-1,and that its rank and idempotent rank are both equal to 2n-1.