On the reduction of associate classes for the PBB designs

Henryk Brzeskwiniewicz

Statistics & Probability Letters, 1991, vol. 11, issue 4, 327-330

Abstract: Necessary and sufficient conditions for the reduction of associate classes in PBB designs are given. The conditions are expressed in terms of the latent roots of the C-matrix of the design and of the association matrices. They are the complement of the result given by Kageyama (1974a). This work contains also a proof that any PBB design whose C-matrix has two different off-diagonal elements and two different latent roots (not including the latent root corresponding to the latent vector composed of ones) is a PBB design with two associate classes. This generalizes the analogous results established by Kageyama (1974b, p. 548)

Keywords: PBB; designs; associate; classes; association; scheme; Fp-type; association; scheme (search for similar items in EconPapers)
Date: 1991
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