Notations


In order to formulate things on this and other theoretical pages I need to introduce the following notations:

      T(n)    : magical square of dimension n
      T(n;k)  : semi magical square of dimension n and subconstant k
      T(n,x)  : T(n) each number augmented with x
      T(n;k,x): T(n;k) each number augmented with x



(I use 'T' since it is the first letter of the dutch Tovervierkant (meaning Magic Square),
'M' and 'S' I have in use for a general matrix and the swapping matrix) Simular I have:

      C(n)    : magical cube of dimension n
      C(n;k)  : semi magical cube of dimension n with subconstant k
      C(n,x)  : C(n) each number augmented with x
      C(n;k,x): C(n;k) each number augmented with x



With T(n;k) and C(n;k) I include T(2;1) and C(2;1) into my theories (order 2 squares or
cubes don't exist)



Summary of used matrices:






      O(n) : the odd Oii == 1 if i odd ; rest 0
      E(n) : the even Eii == 1 if i even; rest 0
      S(n) : the swap Si,n+1-i == 1 i == 1..n; rest 0



the odd and even are thus defined that the expressions:

      O M O + E M E == Mij ((i + j) even)
      O M E + E M O == Mij ((i + j) odd) 



I'm sure odd, even and swap holors can be defined to act simular on cubes



In the various pages of this work the following notations are introduced:

    [pos]Corder(V0)(V1)(V2) : cube of given order, generated by the given knightjump
                             vectors starting from pos
               C3a,b,c,d : cube of order 3,
                             with the numbers a,b,c and d int the upper left of 
                             the front face



In the knight-jump notation for pan(...)agonal (hyper) cubes drop the pos (it doesn't mather), the amount of vectors involved 
as well as the form of the vectors depend on the spatial dimension 'dim'