User blog:Ynought/Extended array hierarchy

If you havent seen the original one here it is:[//googology.wikia.com/wiki/User_blog:Ynought/Array_hierarchy https://googology.wikia.com/wiki/User_blog:Ynought/Array_hierarchy]

\(\bullet\) is anything that is already well defined at that point

any 0 gets deleted

\((\bullet)_{\bullet_20\bullet_3}=(\bullet)_{\bullet_2\bullet_3}\)

\((a,b…,d)_{e,f…,g}=((a+d,b+d...,d+d),...(a+d,b+d,...,d+d))_{e+d,f+d...,d-1}\)

you can even create stuff like this \((\bullet)_{(\bullet_2)_{\dots_{\bullet_k}}}\)

so now i will be adding a couple of new ideas:

\(a\) is the leftmost non 0 entry in \((\bullet)\) and if there is no non 0 entry then a=1

\((\bullet)^0_{(\bullet_2)}=(\bullet)_{(\bullet)_{\dots_{(\bullet_2)}}}\) with \(a\) nests

or in words:

if the \(k\) (always the number inbetween the two arrows here \((\bullet)^{\rightarrow k \leftarrow}_{\bullet_2}\)    )

if \(k\)=0 then 

1.remove it 

'''2.replace \(\bullet_2\) with the array gained after rule 1. \(a\) times'''

now when k is bigger than one

\((\bullet)^k_{(\bullet_2)}=(\bullet)^{k-1}_{(\bullet)^{k-1}_{(\bullet)^{k-1}_{\dots(\bullet_2)^{k-1}}}}\) with \(a\) nests

or in words when k>0:

1.decrement k by one

'''2.replace \(\bullet_2\) by the array gained after rule 1. a times'''

well now:

\((a,b…,d)^{(e,f…,g)}_\bullet=\)

\(((a+d,b+d...,d+d)^{(e+g,f+g...,g-1)}_\bullet,...,(a+d,b+d...,d+d)^{(e+g,f+g...,g-1))}_\bullet)^{(e+g,f+g...,g-1)}\)