Two-Factor Saturated Designs: Cycles, Gini Index, and State Polytopes.

In this paper 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.