User blog:Ynought/G function

Well i thought about the FGH and how it works so i thought about how to put that into a simple notation.Because of that i came up with the simple \(G\) function

The definition is:

$ is the rest of the notation

a always refers to the number before the \(G\) i.e for \(5G(3)(2)\) \(a=5\)

Start looking from right to left until you find a number then apply the following rules:

\(a G $b=(...((aG $b-1)G $b-1)...aG $b-1)G $b-1\) with a nests

except \(aG $0=a+1G $\)

a is always the number before the \(\#\)

\([\) \(]\) is any amount of brackets

with more than zero brackets \([b]=[b-1]...[b-1]\)

any with more than zero brackets \([0]=[a]\) with one less pair of bracket

And since i like to extend my stuff:

\([ [ b ] \bullet] = [ [ b-1 ] \bullet]\dots[ [ b-1 ] \bullet]\) a nests

\( [b]^1= q\dots q\) with a nests.Where \(q=[...[b]...]\) with a nests

\( [b]^k= q\dots q\) with a nests.where \(q=[...[b]^{k-1}...]^{k-1}\)

here \($\) can also be a stack

\([b]^{$c}=o_{aG\dots$[b]^{$c-1}\dots}...o_{aG\dots[b]^{$c-1}\dots}\) with a nests where \(o_k=o_{k-1}...o_{k-1}\) with a nests and \(o_0=[b]^{$c-1}\dots[b]^{$c-1}\) with a nests

\(($,0)=($)...($)\) with a nests

<p data-parsoid="{"dsr":[2011,2066,0,0]}">and here \((_k^$\) means \((^$\dots(^$\) with a \((\)'s

<p data-parsoid="{"dsr":[2068,2125,0,0]}">and here \^$_k\) means \^$\dots)^$\) with a \^$\)'s

<p data-parsoid="{"dsr":[2127,2210,0,0]}">and \(k_n\) means replaceing k by the current system (without the \(aG\) ) n times

<p data-parsoid="{"dsr":[2212,2407,0,0]}">\((b,c,d,e...f)=(y,y,y,y...,f-1)...(y,y,y,y...,f-1)\) a nests and \(y=((_kb_a)^{(b,c,d,e...f-1)}_k,(_kc_a)^{(b,c,d,e...f-1)}_k...,f-1)\) with all the element in the original array being effected.