Question: (i) Consider the following recursive definition of 3-PERMUTATION: Rule 1 123 is a 3-PERMUTATION. Rule 2 If xyz is a 3-PERMUTATION, then so are zyx

(i) Consider the following recursive definition of 3-PERMUTATION:
Rule 1 123 is a 3-PERMUTATION.
Rule 2 If xyz is a 3-PERMUTATION, then so are zyx and yzx.
Show that there are six different 3-PERMUTATIONs.
(ii) Consider the following recursive definition of 4-PERMUTATION:
Rule 1 1234 is a 4-PERMUTATION.
Rule 2 If xyzw is a 4-PERMUTATION, then so are wzyx and yzwx.
How many 4-PERMUTATIONs are there (by this definition)?

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