Let Pn be the partial transformation semigroup on Xn={ 1,2,…,n}.Let 1 ≤ r≤n,put PF(n,r)={α∈Pn:iα=i,(V)i∈dom(α)∩{1,2,…,r}},it is obvious that the semigroup PF(n,r)is subsemigroup of Pn.In this paper,we shall study the rank of the semigroup PF(n,r),where 1 ≤r≤n-1.For n≥3,we prove that rank(PF(n,r))={2+2r,n-r=1,3+2r,n-r=2,4+2r,n-r≥3.
partial transformation semigroupfixed setrankgenerating set
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