however since these kind of vector spaces omit the basic requirement of regular magic squares for the participating squares entries (the numbers) for being unique within a given square, this let me to the idea of putting in some number generating function, besides that one might also consider some variations on the 'magic-condition' (as one also has in regular magic squares, where one has 'semi-magic' (off diagonal sums) and 'semi magic' squares (block-wise of sums)) this leads to the general magic objects defined as:

n: The order of the object

with: G = IC, IR, IQ, IZ, IN

Object: Square, Cube, Tesseract ....

f(): number generating function

g(): 'magic condition'

See the item

and the item 'f() and g()' for remarks on the numbergenerating function f()

as well as on the magic condition g()!

Yet unclear how these objects will evolve, but it is I think worth investigating

If you want to participate in further investigation of the subject, one can do this through email, or create a page of your own (Email me the URL, I'll then have that URL in onto my pages)

for the moment my email contact (who wants to be anonymous) and I worked out the

as the third order 'matrix' vector space, some quite interesting quations hoever remain open for the moment, since I nor mentioned email contact worked with 'matrix'-vector spaces

The regular magic squares can be defined in terms of the above as

is the main item discusses in my Magic squares and cubes

The p MultiMagic squares can be defined in terms of the above as

(the above defines p seperate magic squares)

in the above examples 'sums' means of course all sums horizontally, vertically,

and along both diagonals