The preceding problem establishes a 1 : 1 correspondence between e − 1 permutations T of G0 which are not the identity and e − 1 nonempty subsets

{i1,...,ir} of the set {1,..., n}. If the permutations T and T  correspond respectively to the subsets R = {i1,...,ir} and R = {j1,..., js}, then the group product T 

T corresponds to the subset (R ∩ S˜) ∪ (R˜ ∩ S) = (R ∪ S) − (R ∩ S). [Hartigan

(1969).]