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

  • Roberto FontanaEmail author
  • Fabio Rapallo
  • Maria-Piera Rogantin
Article

Abstract

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.

Keywords

Estimability Gini index State polytope Universal Markov basis 

AMS Subject Classification

62K15 15B34 05B20 62H17 

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Copyright information

© Grace Scientific Publishing 2014

Authors and Affiliations

  • Roberto Fontana
    • 1
    Email author
  • Fabio Rapallo
    • 2
  • Maria-Piera Rogantin
    • 3
  1. 1.Department of Mathematical SciencesPolitecnico di TorinoTurinItaly
  2. 2.Department DISITUniversità del Piemonte OrientaleAlessandriaItaly
  3. 3.Dipartimento di MatematicaUniversità di GenovaGenovaItaly

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