I got my head in a little twist over this whole thread. Reassure me: do all the different parethesizations of 3^3^3^...^3, for n 3's, give different values? The original problem (using principle values of a^b) is interesting because i is special, right? On Wed, Nov 29, 2017 at 9:46 AM, James Propp <jamespropp@gmail.com> wrote:
Apropos of parenthesizing exponential towers, here's an easier question (probably not new): Look at all the (Catalan-many) ways to parenthesize a_1 - a_2 - ... - a_n. Not all are distinct as linear functions of a_1, a_2, ..., a_n; e.g.,
(a - (b - c)) - d = a - (b - (c - d)).
How many different functions can be obtained? I don't know the answer. Is it 2^(n-2)?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun