At 03:33 AM 11/30/2000 -0800, Daniel Yoo wrote:

There was a question about ways of generating permutations: is there an easy way to show that these two functions:

<<SNIP>>

act differently?

They have different properties. There's only one possible route to ABCD...WXYZ in the restricted method (all letters self-identified) through a narrowing set of options at each turn, for 26 turns. But the unrestricted method gives a great many pathways to this same terminus in 26 iterations, by presenting a non-narrowing set of options at each turn. The restricted method is your classic decision tree with fanning branches, terminating in 26! equally probable outcomes. Every iteration forces you to the next level, towards the final outcome level. The unrestricted method allows you to retrace your steps, back towards the beginning. Without trying to compute a lot of specific probabilities, I think you can see that the two methods, while confined to the same "state space" of 26! letter sequences, are not isomorphic (i.e. are not simply two ways of doing the exact same thing). Kirby