[seqfan] Re: Intersections of x^x^...^x

[Andrew Weimholt]

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