Permutations, Derivative Hierarchy

PERMUTATION GROUPS 1-4 – DERIVATIVE HIERARCHY

1
1 2
1 2 3
1 2 3 4
1 2 4 3
1 4 2 3
4 1 2 3
1 3 2
1 3 2 4
1 3 4 2
1 4 3 2
4 1 3 2
3 1 2
3 1 2 4
3 1 4 2
3 4 1 2
4 3 1 2
2 1
2 1 3
2 1 3 4
2 1 4 3
2 4 1 3
4 2 1 3
2 3 1
2 3 1 4
2 3 4 1
2 4 3 1
4 2 3 1
3 2 1
3 2 1 4
3 2 4 1
3 4 2 1
4 3 2 1

Does this have any important mathematical significance? Well, no, not really. Yes, it shows clearly why there are n! permutations of n, but you knew that already. So why bother with it? Because, think of this list, not of 1-4, but 1-infinity. Can you visualize it? It is infinite in a rather complex way.