User blog comment:Alejandro Magno/Extended Arrow Notation/@comment-5029411-20140920203940

^(n)^(m)^(n)^ is shorten into ^(n)(m)^

^(n)^(m)^(n)^(l)^(n)^(m)^(n)^ is shorten into ^(n)(m)(l)^

...

^(n)^(2)^ = ^(n)(n)...(n)(n)^ /w n (n)'s

^(n)(2)^(2)^ = ^(^(n)(n)...(n)(n)^(2)^)^(2)^ /w n (n)'s

^(n)^(m)^ = ^(n)(n)...(n)(n)^(m-1)^ /w n (n)'s

^(n)^(m)^(l)^ = ^(n)^(m)(m)...(m)(m)^(l-1)^ /w m (m)'s

^(n)^^(m)^ = ^(n)^(n)...(n)^(n)^^(m-1)^ /w n (n)'s

^(n){^(l)^}(m)^ = ^(n){^^...^^}(m)^ /w l up-arrow's

The limit of extension is ^{^{^{...}^}^}^ operator