all transpositions: (12) (13) (14) (23) (24) (34) all permutations: d=0 [1, 2, 3, 4] d=1 [2, 1, 3, 4] == (12) on [1, 2, 3, 4] d=1 [3, 2, 1, 4] == (13) on [1, 2, 3, 4] d=1 [4, 2, 3, 1] == (14) on [1, 2, 3, 4] d=1 [1, 3, 2, 4] == (23) on [1, 2, 3, 4] d=1 [1, 4, 3, 2] == (24) on [1, 2, 3, 4] d=1 [1, 2, 4, 3] == (34) on [1, 2, 3, 4] d=2 [2, 3, 1, 4] == (13) on [2, 1, 3, 4] == (12) on [1, 2, 3, 4] d=2 [2, 4, 3, 1] == (14) on [2, 1, 3, 4] == (12) on [1, 2, 3, 4] d=2 [3, 1, 2, 4] == (23) on [2, 1, 3, 4] == (12) on [1, 2, 3, 4] d=2 [4, 1, 3, 2] == (24) on [2, 1, 3, 4] == (12) on [1, 2, 3, 4] d=2 [2, 1, 4, 3] == (34) on [2, 1, 3, 4] == (12) on [1, 2, 3, 4] d=2 [3, 2, 4, 1] == (14) on [3, 2, 1, 4] == (13) on [1, 2, 3, 4] d=2 [3, 4, 1, 2] == (24) on [3, 2, 1, 4] == (13) on [1, 2, 3, 4] d=2 [4, 2, 1, 3] == (34) on [3, 2, 1, 4] == (13) on [1, 2, 3, 4] d=2 [4, 3, 2, 1] == (23) on [4, 2, 3, 1] == (14) on [1, 2, 3, 4] d=2 [1, 3, 4, 2] == (24) on [1, 3, 2, 4] == (23) on [1, 2, 3, 4] d=2 [1, 4, 2, 3] == (34) on [1, 3, 2, 4] == (23) on [1, 2, 3, 4] d=3 [2, 3, 4, 1] == (14) on [2, 3, 1, 4] == (13) on [2, 1, 3, 4] == (12) on [1, 2, 3, 4] d=3 [4, 3, 1, 2] == (24) on [2, 3, 1, 4] == (13) on [2, 1, 3, 4] == (12) on [1, 2, 3, 4] d=3 [2, 4, 1, 3] == (34) on [2, 3, 1, 4] == (13) on [2, 1, 3, 4] == (12) on [1, 2, 3, 4] d=3 [3, 4, 2, 1] == (23) on [2, 4, 3, 1] == (14) on [2, 1, 3, 4] == (12) on [1, 2, 3, 4] d=3 [3, 1, 4, 2] == (24) on [3, 1, 2, 4] == (23) on [2, 1, 3, 4] == (12) on [1, 2, 3, 4] d=3 [4, 1, 2, 3] == (34) on [3, 1, 2, 4] == (23) on [2, 1, 3, 4] == (12) on [1, 2, 3, 4] distance counts 0 1 1 6 2 11 3 6