Classification of combined action of binary factors and Coxeter groups

Abstract

A general model of an experiment with a finite number of two-level factors and a two-level outcome is considered. Joint action types are identified within the formalism developed. It is shown that the experiment can be represented by a free Boolean algebra and the identification of joint action types in this experiment reduces to the study of action orbits of an automorphism group over the Boolean algebra. Two types of symmetries are considered, and related classifications are provided.