Graham Array Notation

The Graham Array Notation is a Googological Notation devised by Antares Harrison

Basics
At the core of this notation is Arrow notation and BEAF.

Arrays
"Arrays" are lists of numbers. An example is \(\ [3,3,4,4,4]\)

Arrays, like BEAF, Bird's array notation or Hyperfactorial array notation, can be multidimensional or multirowed.

Rules
Rule 6 : [a,b,c,d,e] = [[a,b,c,d],[a,b,c,d],e]


 * 6-1 : [a,b,c,d,e,f,g,h] = [[a,b,c,d,e,f],[a,b,c,d,e,f],g,h]


 * 6-2 : [a,b,c,d,e,f,g,h,i] = [[a,b,c,d,e,f,g,h],[a,b,c,d,e,f,g,h],i]


 * 6-3 : [a,b,c,d,e,f,g,h,i,j] = [[a,b,c,d,e,f,g,h],[a,b,c,d,e,f,g,h],i,j]

Rule 7 : [a,b,c,d,e,f] = [[a,b,c,d],[a,b,c,d],e,f]
 * 6-4 : [a,b,c,d,e,f,g,h,i,j,k] = [[a,b,c,d,e,f,g,h,i,j],[a,b,c,d,e,f,g,h,i,j],k]

Rule 8 : [a,b,c,d,e,f,g] = [[a,b,c,d,e,f],[a,b,c,d,e,f],g]

Rule 9 : [a,(b)] = [a,[a,(b-1)]]

If I am right, Rule 9 is about a^^b+2

Rule 10 : [a,b,(c)] = [a,b,[a,b,(c-1)]]

If I am right, Rule 10 is about [a,b,b,c+1]

Rule 11 : [#,(a)] = [#,[#,(a-1)]]

Rule 12 : A 2-dimensional Array of a,b (If you can imagine it, I can't wikitext) like would be [a,b]^[a,b]. We will get to the ^ later on.

Rule 13 : [a^b] = [a,a,a,......a,a] (b times)

Rule 14 : [a^^b] = [a^a^a^a......^a^a] (b times)

Rule 15 : [a{^}b] = [a^^^......^^^b] (b ^'s)

Rule 16 : [a{[^}}b] = [a{^}a{^}a{^}a......{^}a{^}a] (b times)

Rule 17 : [ab] = An c-dimensional array of [a,b] (BEAF's ab & c)

Rule 18 : [ab] = An c-dimensional array of [a,b] with the side lenght d, counting the array as a lenght of 1.

Rule 19 : Any array can be (c)-ed, be multidimensional, and so on

Rule 20 : [a,b]c = [ab] with c {}'s.

Rule 21 : [a,b/c] = [a,b]c

Rule 22 : [a,b/c,d] = [....[a,b,[a,b,[a,b]c]c]....] with d []'s

Rule 23 : [A,b] = [b,b/b,b]

Rule 24 : [A,b]3 = [b,b,b/b,b]

Rule 25 : [A2,b] = [b,b/b,[b,b/b,b]]

Rule 26 : [An,b] = [b,b/b,[b.......[b,b/b,[b,b/b,b]].......]] with n []'s

Dimensional Arrays
2-Dimensional arrays are multi-rowed arrays. These are done by [a<2>b]. That would be a two-row aray. (I can't use wikitext). It's like BEAF. If [a,<2/n>b], that would be a n-row array. As we said, arrays are connected by the ^.

3-dimensional arrays are cubic arrays. These are 2-dimensional array connected by ^'s. If [a<3/n>b], like 2-dimensional arrays, these would be a n-row array piled up in 3-dimensional space n times, connected by a ^.

This is the same for n-dimensional array, n-1 dimensional arrays connected with a ^. If [ab], that would be n-1 dimensional arrays with the side lenght m for all dimensions.

This may be a little difficult to understand. Please imagine BEAF's arrays as an example.

External Sources
[googology.weebly.com|Wesite]

Read More

 * Bird's array notation
 * BEAF
 * HAN
 * Extensible-E System