User blog:Alejandro Magno/Weak BEAF

Linear Arrays
{n}(weak) = n

{n,m}(weak) = n+m

{x,y,z}(weak) = x+y+z

{a,b,c,...,x,y,z}(weak) = a+b+c+...+x+y+z

SGH
{n}(weak) = g_w(n)

{n,m}(weak) = g_w*2(n)

{x,y,z}(weak) = g_w*3(n)

{a,b,c,...,x,y,z}(weak) = g_w*m(n), where m is the number of entries

So linear array notation has limit of g_w^2(n)

Planar Arrays
{a(1)b}(weak) = {a,a,a,...,a,a,a}(weak) with b entries = a*b

{n,m(1)b}(weak) = {n+m(1)b}(weak)

...

{a(1)b,c}(weak) = {a(1)b+c}(weak)

...

{a(1)b(1)c}(weak) = {a(1)b,b,b,...,b,b,b}(weak) with b entries

...

SGH
{a(1)b}(weak) = g_w*w(n)

{a(1)b,c}(weak) = g_w*(w+w)(n)

{a(1)b(1)c}(weak) = g_w*(w*w)(n)

So planar arrays have a limit of g_w^w(n)

Dimensional Array Notation
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