Counting functions of magic labelings

A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum, the magic sum. The most famous class of examples are magic squares (the sets are the rows, columns, and diagonals of a matrix). It follows from a recent paper by Matthias Beck and Thomas Zaslavky that the number of n by n magic labellings is a quasipolynomial function of the magic sum, and also of an upper bound on the entries in the square. The contribution of this thesis is to develop software that allows computation of a large class of examples of generating functions for such counting functions. The software will utilize previously developed programs THAC (developed at SFSU) and Latte (developed at UC Davis) to compute intermediate results required by the overall computation. The symbolic algebra program Maple (developed at the University of Waterloo, Canada) will be used for final algebraic manipulation to achieve the final result which is the generating function of a counting function. While there are other methods to compute these types of counting functions, it is believed that the approach used in this thesis is novel and no such software exists.