Can you prove that for every Almida framework, no two paths ever
end up at the foot of the same upright? We have to show that the
system described is a permutation (re-arrangement) of the numbers 1
to n which occur at the top of the uprights.
Imagine moving
numbered counters down the paths at the same rate and every time a
rung is encountered the two counters on adjacent uprights change
places; this is called a transposition.
This is a good way of recording the sequence transpositions
12345
21345
21354
23154
23514
32514
32541
35241
35214
35124
53124