On the idempotent ranks of the semigroup V(n,r)
Ping Zhao · Journal of Shandong University · 2012
Let SPCn be the semigroup of all strictly decreasing and order-preserving partial transformations on [n].For n≥5 and 2≤r≤n-2,we show that the subsemigroup V(n,r)={α∈SPCn:|im(α)|≤r} is idempotent-generated,with both rank and idempotent rank are equal to sum from n-1 to k=r((nk)(k-1 r-1)).