A Characterization of Saturated Designs for Factorial Experiments

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In this paper we study saturated fractions of factorial designs under the perspective of Algebraic Statistics. Exploiting the identification of a fraction with a binary contingency table, we define a criterion to check whether a fraction is saturated or not with respect to a given model. The proposed criterion is based on combinatorial algebraic objects, namely the circuit basis of the toric ideal associated to the design matrix of the model.

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