Universal Gröbner Bases for Designs of Experiments

Universal Gröbner bases (UGB) are a useful tool to obtain a set of different models identified by an experimental design. Usually, the algorithms to obtain a UGB for the ideal of a design are computationally intensive. Babson et al. (2003) propose a methodology to construct UGB in polynomial time. Their methodology constructs a list of term orders based upon the Hilbert zonotope. We focus on the generation of such a list. We use results on hyperplane arrangements to present a theorem which simplifies the computation of term orders for designs in two dimensions. Our theorem constructs directly the normal fan of the Hilbert zonotope.