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Wednesday, December 12, 2007

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.

3 comments:

  1. shonk9:52 PM

    Cantor set?

    ReplyDelete
  2. "I've gone cross eyed."--Austin Powers

    ReplyDelete
  3. Dear shonk,

    I don't think you can create an equivalent of the Cantor set that is discrete, as this is.

    ReplyDelete