User blog comment:Cookiefonster/Analysis of Graham Array Notation - is it well-defined?/@comment-27173506-20160103171733

I've tried to do an analysis by filling in the gaps:

1. If the number of entries is odd: [#,z]=[[#],[#],z]

2. If the number of entries is even: [#,y,z]=[[#],[#],y,z]

3. [#a^b]=[#a,a,a...a,a] with b a's

4. [#a^n+1 b]=[#a^ n[a^n[a^...[a^na]]...]] with b a's

5. [#a{^}b]=[#a^ba]

6. [#a{n+1^}n+1b]=[#a{n^}na{n^}na{n^}na...a{n^}na] with b a's

The collapsing of linear arrays is so weak that [n,n,n...n,n] with m entries is approximately f_w+1[^m](n) (because each entry adds 1 iteration), so [n^n]~f_w+2(n).

[n^^n]~f_w+3

[n{^}m]~f_w+m+2(n)

[n n]~f_w2+1(n)

[n,n]m~f_w2+m(n)

[n,n]n~f_w3

[n,n/n,n]~f_w3+1

So with all the ambiguity solved, it still only reached f_w3+1(n). Well, maybe the dimensional arrays would have done better, but I won't even try to decipher them.