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November, 1974 On the Reduction of Associate Classes for the PBIB Design of a Certain Generalized Type
Sanpei Kageyama
Ann. Statist. 2(6): 1346-1350 (November, 1974). DOI: 10.1214/aos/1176342889

Abstract

For BIB designs $N_i$ and their complements $N_i^\ast (i = 1,2, \cdots, n)$, Kageyama (1972) gave necessary and sufficient conditions for a PBIB design $N = N_1 \otimes N_2 + N_1^\ast \otimes N_2^\ast$ with at most three associate classes having the rectangular association scheme to be reducible to a PBIB design with only two distinct associate classes having the $L_2$ association scheme. In this paper similar results for the PBIB design $N_1 \otimes N_2 \otimes \cdots \otimes N_n + N_1^\ast \otimes N_2^\ast \otimes \cdots \otimes N_n^\ast$, which is in a sense a generalization of the Kronecker products of the above type, are described.

Citation

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Sanpei Kageyama. "On the Reduction of Associate Classes for the PBIB Design of a Certain Generalized Type." Ann. Statist. 2 (6) 1346 - 1350, November, 1974. https://doi.org/10.1214/aos/1176342889

Information

Published: November, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0295.62085
MathSciNet: MR398018
Digital Object Identifier: 10.1214/aos/1176342889

Subjects:
Primary: 62K10
Secondary: 05B20

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 6 • November, 1974
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