04/27/2008, 07:17 AM

I was wondering why left and balanced are not being talked about here too much since they obviously give different results when iterated. There is also a possibility to make a mix of them as well on a way, changing bracketing in the middle of sequences, or any place, or changing it continuously.

Probably(?) the problem is that there is fast multiplying of different results and not satisfactoy simple way to describe the various infinite trees or paths arising.

My intuitive guess is that there either already exists in mathematics way to describe relations between different values obtained by different bracketing,(trees? tree generating series?) or , if not, especially in continuous extension of iterations, such has to be found, which is probably as very difficult task. But You know that I am not so good in details, so excuse me for having such general views.

Ivars

Probably(?) the problem is that there is fast multiplying of different results and not satisfactoy simple way to describe the various infinite trees or paths arising.

My intuitive guess is that there either already exists in mathematics way to describe relations between different values obtained by different bracketing,(trees? tree generating series?) or , if not, especially in continuous extension of iterations, such has to be found, which is probably as very difficult task. But You know that I am not so good in details, so excuse me for having such general views.

Ivars