It is known that a Markov basis of the binary graph model of a graph $G$ corresponds to a set of binomial generators of cut ideals $I_{ \widehat{ G}}$ of the suspension $\widehat{ G}$ of $G$. In this paper, we give another application of cut ideals to statistics. We show that a set of binomial generators of cut ideals is a Markov basis of some regular two-level fractional factorial design. As application, we give a Markov basis of degree 2 for designs defined by at most two relations.
Categories: math.ST math.AC stat.TH