Using computational algebraic geometry techniques and Hilbert bases of polyhedral cones we derive explicit formulas and generating functions for the number of magic squares and magic cubes. Magic cubes and squares are very popular combinatorial objects (see [2, 15, 17] and their references). A magic square is a square matrix whose entries are nonnegativeâ€¦ (More)

In this paper, we study Absolute Parallelism (AP-) geometry on the tangent bundle T M of a manifold M. Accordingly, all geometric objects defined in this geometry are not only functions of the positional argument x, but also depend on the directional argument y. Moreover, many new geometric objects, which have no counterpart in the classical AP-geometry,â€¦ (More)