User blog comment:Hyp cos/BEAF isn't so strong/@comment-5029411-20130925221644/@comment-11227630-20130927110555

[L,X/2]=L[&]L[&]L...[&]L[&]L - n times, and it's also the limit of original BEAN. So {[L,X/2]}n,n has growth rate θ(ΩΩ2) (see above). If L is type-1 legion and {}-arrays are type-1 arrays, [L,X/2] will be type-2 legion, and it's represented by L2 in legiattic arrays, []-arrays will be type-2 arrays. Generally speaking, the base number of type-n+1 array is always Ln, which means a type-n legion.

And I will add those soon.