61. The preceding problem establishes a 1 : 1 correspondence between e - 1 permutations T of Go which are not the identity and e - 1 nonempty subsets {il , ... , if} of the set {I, ... , n}. If the permutations T and T' correspond respectively to the subsets R = {i1, . . . , if} and R' = {il, .. . . i,}. then the group product T'Tcorresponds to the subset (R ().5) U (R () S) = (R U S) - (R () S). [Hartigan (1969).]