User blog comment:XXxKennyDashxXx/Basic Linear Array Separator Matrix Notation/@comment-30118230-20161025184851

I can see the next extention coming....

(0,0,0)~gamma_0

(0,1,0)=(0,0,(0,0,(0,0,(....(0,0)))))~gamma_1

(0,n,0)~gamma_n

(1,0,0)=(0,(0,(0,(0,(....(0,(0,(0,0),0),0),0),0).....),0),0),0)~gamma_gamma_0

(1,1,0)=(1,0,(1,0,(1,0,(....(1,0,(1,0,(1,0,(1,0))....))))~gamma_gamma_1

(2,0,0)~phi(1,1,0)

(n,0,0)~phi(1,n-1,0)

It seems to become quite similar to the veblen hierarchy.