I stumbled upon idea of tetra factorial in another thread Tetra-factorial, which galathea kindly expanded there into infinity of options, related to rates of growth of functions.
tetra-factorial is in my language \( n(4)!= 2^{3^{4^{...n}}} \)
I was looking for combinatorial content of such factorial and found that according to quickfur here:
The Exploding tree function
It seems that tetra factorial could be related to branching tree chain combinatorics . Quickfur even has series similar to Ramanujan in his paper:
Further, in his thread, quickfur relates these growth rates to Cantor ordinals.
Tetration and higher order operations on transfinite ordinals
Now, despite all this, I have to confess I have problem understanding even the basic ideas in his branching tree paper. When searching on interenet, i also could not hit a BASIC source that would explain the terminology, at least, and also give introduction to the combinatorics of such trees.
Could someone please give some advice where to look or what to search for in internet?
Ivars
tetra-factorial is in my language \( n(4)!= 2^{3^{4^{...n}}} \)
I was looking for combinatorial content of such factorial and found that according to quickfur here:
The Exploding tree function
It seems that tetra factorial could be related to branching tree chain combinatorics . Quickfur even has series similar to Ramanujan in his paper:
Quote:This in turn transforms into a chain of length \( (m^{2m})^{2m^{2m}} + m^{2m} = m^{2m^{2m+1}} + m^{2m} \)..
Further, in his thread, quickfur relates these growth rates to Cantor ordinals.
Tetration and higher order operations on transfinite ordinals
Now, despite all this, I have to confess I have problem understanding even the basic ideas in his branching tree paper. When searching on interenet, i also could not hit a BASIC source that would explain the terminology, at least, and also give introduction to the combinatorics of such trees.
Could someone please give some advice where to look or what to search for in internet?
Ivars
