Mathematical crystal growth I

AbstractLet A, D be finite subsets of Zk (the set of all k-tuples of integers), and consider the sequence of sets (A, A + D, A + D + D,…) which can be thought of growth in a crystal. One starts with a hub A and adds increments equal to D. We represent finite subsets of Zk by means of polynomials, and show that the sequence of polynomials corresponding to the crystal sequence is generated by a rational function. The proof is non-constructive