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Tetrational Arrays up to X^^n.

Gang-Dimensional Arrays

(0,1) = (X) X^X
(n,1) X^(X+n)
(0,n) = (X,n-1) X^(X*n)
(n,m) X^((X*m)+n)

Hypercubed-Dimensional Arrays

(0,0,1) = (X,X) X^X^2
(n,m,k) X^(((X^2)*k)+(X*m)+n)
(0,0,...n 0's...,0,0,1) = (0,0,...n-1 0's...,0,0,X) X^X^n
(a,...,z) X^(a+...+(z*X^n))

Infinite-Dimensional Arrays

((1)1) = (0,0,...X 0's...,0,0,1) X^X^X
(1(1)1) X^((X^X)+1)
(0,1(1)1) = (X(1)1) X^((X^X)+X)
(0,0,1(1)1) = (X,X(1)1) X^((X^X)+X^2)
((1)2) = (0,...X 0's...,0,1(1)1) X^((X^X)*2)
((1)3) = (0,...X 0's...,0,1(1)2) X^((X^X)*3)
((1)0,1) = ((1)X) X^X^(X+1)
((1)(1)1) = ((1)0,...X 0's...,0,1) X^X^(X*2)
((1)1(1)1) = (0,...X 0's...,0,1(1)(1)1) X^(X^(X*2)+X)
((1)(1)(1)1) = ((1)(1)0,...X 0's...,0,1) X^X^(X*3)
((2)1) = ((1)(1)...X (1)'s...(1)(1)1) X^X^X^2
(1(2)1) X^((X^X^2)+1)
(0,1(2)1) = (X(1)1) X^((X^X^2)+X)
(0,0,1(2)1) = (X,X(1)1) X^((X^X^2)+X^2)
((1)1(2)1) = (X,X(1)1) X^((X^X^2)+X^X)

Power-Dimensional Arrays

((2)2) = ((1)(1)...X (1)'s...(1)(1)1(2)1) X^((X^X^2)*2)
((2)3) = ((1)(1)...X (1)'s...(1)(1)1(2)2) X^((X^X^2)*3)
((2)0,1) = ((2)X) X^X^((X^2)+1)
(4,2(1)6,7(1)7,8(2)7,8,5) X^(4+(2*X)+(6*X^X)+(7*X^(X+1))+(7*X^(2*X))+(8*X^((2*X)+1))+(7*X^X^2)+(8*X^((X^2)+1))+(6*X^((X^2)+2)))
((2)(1)1) = ((2)0,...X 0's...,0,1) X^X^((X^2)+X)
((2)1(1)1) = ((1)(1)...X (1)'s...(1)(1)1(2)(1)1) X^((X^((X^2+X))+X))
((2)2(1)1) = ((1)(1)...X (1)'s...(1)(1)1(2)1(1)1) X^((X^((X^2+X))+X*2))
((2)0,1(1)1) = ((2)X(1)1) X^(X^((X^2)+X)+X^2)
((2)(1)2) = ((2)0,...X 0's...,0,1(1)1) X^X^((X^2)+X)
((2)(2)1) = ((2)(1)(1)...X (1)'s...(1)(1)1) X^X^((X^2)*2)
((3)1) = ((2)(2)...X (2)'s...(2)(2)1) X^X^X^3

Eplision-Dimensional Arrays

((0,1)1) = ((X)1) X^X^X^X
(((1)1)1) = ((0,0,...X 0's...,0,0,1)1) X^X^X^X^X
(((0,1)1)1) = (((X)1)1) X^X^X^X^X^X

We need tetrational rules.

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