Enumeration of Integer Lattice Points, with Applications

In this paper, we will use generating functions as a tool to examine\ud three related problems, which can all be expressed in terms of finding natural number solutions to a system of linear equations. We will consider the enumeration of integer lattice points in a polyhedral cone, the\ud enumeration of magic squares, and the enumeration of magic labellings of a pseudograph. Although we will discuss these topics each separately, the work throughout the paper will demonstrate how these seemingly disparate topics are related