| A magic square is an n x n matrix with non-negative integer entries, such that the sum of the entries in each row and column is the same. We study the enumeration and P-recursivity of these in the case in which the sum along each row and column is fixed, with the size n of the matrix as the variable. A method is developed that nicely proves some known results about the case when the row and column sum is 2, and we prove new results for the case when the sum is 3.; The second part of the dissertation deals with magic cubes, about which almost nothing is known. We apply a theorem from graph theory to get an initial result in a new direction on magic cubes, that of completion. That is, after realizing the inherent connection between magic cubes and Latin Squares, we prove a condition which guarantees that a partially complete magic cube can be completed. |
