Majorization and applications to block designs

Abstract

Majorization is a partial ordering on vectors which determines the degree of similarity between the vector elements. In this paper the majorization technique is employed for the comparison of the eigenvalue n-tuples of the C-matrices of two competing designs. Designs which are optimal in the sense of majorization are presented. Further, M-optimality is revealed as a generalised optimality criterion. The application of majorization in checking the existence of designs is also presented.