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