## Factorial Designs and Harmonic Analysis on Finite Abelian Groups

Lecturer: Peter van de Ven

 In this talk we discuss factorial designs within the algebraic framework of harmonic analysis on finite abelian groups. Factorial designs are widely used for experiments in which the influence of multiple input variables on an experimental outcome is of interest. Designs in this class are constructed using a fixed set of settings for each variable. Any combination of settings of the variables is known as a treatment combination. A full factorial design is a factorial design involving all possible treatment combinations. The treatment combinations in a full factorial design have traditionally been coded using the elements of a finite abelian group. If the number of variables is large then full factorial designs can become quite costly. In those cases typically only a subset of the treatment combinations is used in the experiment. Such a subset is usually referred to as a fractional factorial design or a fraction. Regular fractions are a special class of fractional factorial designs. Within the group-theoretic framework a regular fraction is defined as the coset of a finite abelian group. However, several other definitions for regular fraction appear in literature. We use the character theory of finite abelian groups to show the equivalence of the definitions and to derive specific properties of regular fractions.