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Aug 24, 2010 at 23:03 comment added Ben Golub Thanks very much for your answer. I should have been clearer in the question, but it is important to me not to use the standard Prüfer sequence way of generating random trees, but rather to "build up" -- which is why I introduced the function f. The reason for my desiderata is that I have a decomposition procedure that splits up T into a bunch of pieces (satisfying certain conditions). It is easy to see how this decomposition ``evolves'' when you add in a vertex and attach it in some simple way, but very hard to do the decomposition straight from a random Prufer sequence.
Aug 24, 2010 at 17:42 history answered Mitch CC BY-SA 2.5