Aai wrote: > The second idea is based on analyzing the pattern of the conn. matrix. > Starting with dimension 3, the c.m. can be constructed with the two sub > matrices M and I: > > 0 1 0 1 1 0 0 0 > 1 0 1 0 0 1 0 0 > 0 1 0 1 0 0 1 0 > M= 1 0 1 0 0 0 0 1 > 1 0 0 0 0 1 0 1 > 0 1 0 0 1 0 1 0 > 0 0 1 0 0 1 0 1 > 0 0 0 1 1 0 1 0 >
Is this the connection matrix on the edge graph? If so, you can get it in general as follows: For an n-cube, label the vertices with the numbers i.2^n by regarding the cube as the unit cube in R^n. Any two vertices are connected by an edge if and only if their coordinates differ by 1 in exactly one place. So, f=:1=+/@: | @: - f"1/~ #: i.2^3 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 (Slightly different labelling from yours, but I think the same thing.) This only deals with edge graphs. If you want intersections of arbitrary subcubes, you are getting into homology theory, specifically cubical homology. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
