User:Googleaarex/Tetrational Arrays

Linear Arrays
{a} or {a,1,c #} = a, {a,b} = a^b

{# 1} = {#}

{a,b,1,...,1,c #} = {a,a,a,...,a,a,{a,b-1,c},c-1 #} (numbers of of 1's +1 a's)

Dimensional Arrays
{a} or {a,1,c #} = a, {a,b} = a^b {# 1} = {#} {# (n) 1 #} = {#} {a,b,1,...,1,c #} = {a,a,a,...,a,a,{a,b-1,c},c-1 #} (numbers of 1's +1 a's) {a,b (A)(B)...(Y)(Z) c #} = {a  b (A) a b (B)... a  b (Y) a  b (Z) c-1} {a,b (A)(B)...(Y)(Z) 1,1,...,1,1,1,c #} = {a  b (A) a  b (B)... a  b (Y) a  b (Z) a,a,...,a,a,R,c-1} (numbers of 1's -1 a's), where R is {a,b-1 (A)(B)...(Y)(Z) 1,1,...,1,1,1,c #} a <1> b = a,a,...,a,a (b a's) a  1 = a a  b = a  b (c-1) a  b (c-1) ... a  b (c-1) a  b (c-1) a  b (b times)

Tetrational Arrays
Rule 1 : {a} or {a,1,c #} = a, {a,b} = a^b Rule 2 : {# 1} = {#} Rule 3 : {# (n) 1 #} = {#} Rule 4 : {a,b,1,...,1,c #} = {a,a,a,...,a,a,{a,b-1,c},c-1 #} (numbers of 1's +1 a's) Rule 5 : {a,b (A1)(B1)...(Y1)(Z1) c #} = {a  b (A1) a  b (B1)... a <Y1> b (Y1) a <Z1> b (Z1) c-1} Rule 6 : {a,b (A1)(B1)...(Y1)(Z1) 1,1,...,1,1,1,c #} = {a <A1> b (A1) a <B1> b (B1)... a <Y1> b (Y1) a <Z1> b (Z1) a,a,...,a,a,R,c-1} (numbers of 1's -1 a's), where R is {a,b (A1)(B1)...(Y1)(Z1) 1,1,...,1,1,1,c-1 #} a <1> b = a,a,...,a,a (b a's) a <c> 1 = a a <<A2 #><B2 #>...<Y2 #> A1 <Z2 #> B1,C1 #> b = a <<A2 #><B2 #>...<Y2-1 #><Y2-1 #>...b times...<Y2-1 #><Y2-1 #>1 <Z2 #> A1-1 <B2 #> B1,C1 #> b a <# <A2> 0 <B2> #> b = a <# <A2><B2> #> b a <0 #> b = a <#> b a <# <0> #> b = a <# 0 #> b a <# A1,B1,C1,0 #> b = a <# A1,B1,C1 #> b a <# 0,...,0,A1 #> b = a <# b,...,b,A1-1 #> b a <A1> b = a <A1-1> b (A1-1) a <A1-1> b (A1-1) ... a <A1-1> b (A1-1) a <A1-1> b (A1-1) a <A1-1> b (b times)