User blog:Googleaarex/Stronger Hyperfactorial Array Notation

Let change the rule: \(n![\circ 1,m+1 \bullet]\) = \(n![\circ ...[[\circ 1,m \bullet]...,m \bullet]\) (n nested)

\(\circ\) is rows of 1

\(\bullet\) is anything

Growth Rates
[[1] ] has growth rate \(\omega 2\)

[[n] ] has growth rate \(\omega 2 + (n-1)\)

[[[1] ] ] has growth rate \(\omega 3\)

[1,2] has growth rate \(\omega^2\)

[[1],2] has growth rate \(\omega^2 + \omega\)

[[1,2],2] has growth rate \(\omega^2 2\)

[1,3] has growth rate \(\omega^3\)

[1,n] has growth rate \(\omega^n\)

[1,[1]] has growth rate \(\omega^\omega\)

[1,[1,2]] has growth rate \(\omega^{\omega^2}\)

[1,1,2] has growth rate \(\varepsilon_0\)

[[1,1,2],1,2] has growth rate \(\varepsilon_0 2\)

[1,2,2] has growth rate \(\varepsilon_0 \omega\)

[1,[1],2] has growth rate \(\varepsilon_0 \omega^\omega\)

[1,[1,1,2],2] has growth rate \(\varepsilon_0^2\)

More growth rates soon!