The Rank of the Semigroup SPK~-(n,r)
Ping Zhao · Journal of South China Normal University · 2012
Let SPS-n be the semigroup of all strictly decreasing partial transformations on [n].For n≥5 and 3≤ r≤n-2,it is shown that the semigroup SPK-(n,r)={α∈SPS-n:︱im(α)︱≤r} is idempotent-generated,and further both rank and idempotent rank of which are equal to (r+1) S(n,r+1).