Two-factor saturated designs: Cycles, gini index, and state polytopes

In this article, we analyze and characterize the saturated fractions of two-factor designs under the simple effect model. Using linear algebra, we define a criterion to check whether a given fraction is saturated or not. We also compute the number of saturated fractions, providing an alternative proof of the Cayley's formula. Finally, we show how, given a list of saturated fractions, Gini indexes of their margins and the associated state polytopes could be used to classify them.