[seqfan] Re: Intersections of x^x^...^x
Andrew Weimholt
andrew.weimholt at gmail.com
Thu Nov 3 09:08:55 CET 2011
On Wed, Nov 2, 2011 at 7:10 PM, Vladimir Reshetnikov
<v.reshetnikov at gmail.com> wrote:
> Consider a set of functions obtained by all possible parenthesizations of
> x^x^...^x (with n x's). How many pairwise intersections do they have for
> 0<x<1? And for x>1?
>
for n>3, it is infinite...
(x^x)^(x^x) = (x^(x^x))^x
ln ((x^x)^(x^x)) = ln ((x^(x^x))^x)
(x^x) * ln (x^x) = x * ln (x^(x^x))
x*(x^x) * ln (x) = x*(x^x) * ln (x)
QED
Andrew
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