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).]