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July, 1973 Constructions for Some Classes of Neighbor Designs
F. K. Hwang
Ann. Statist. 1(4): 786-790 (July, 1973). DOI: 10.1214/aos/1176342476

Abstract

Rees [2] introduced the concept and name of "neighbor" designs. The problem can be described as that of arranging $v$ kinds of objects on $b$ plates each containing $k$ objects in a loop such that every object on a plate has two neighbors. The requirements are that each object appears $r$ times (but not necessarily on $r$ different plates) and is a neighbor of every other object exactly $\lambda$ times. This paper constructs neighbor designs with parameters as follows: $(i) k > 2:\quad v = 2k + 1, \lambda = 1$ $(ii) k \equiv 0 (\mod 2) > 2:\quad v = 2^i k + 1, i = 1,2,\cdots, \lambda = 1$ $(iii) k \equiv 0 (\mod 4):\quad v = 2mk + 1, m = 1,2,\cdots, \lambda = 1.$

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F. K. Hwang. "Constructions for Some Classes of Neighbor Designs." Ann. Statist. 1 (4) 786 - 790, July, 1973. https://doi.org/10.1214/aos/1176342476

Information

Published: July, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0262.62038
MathSciNet: MR336932
Digital Object Identifier: 10.1214/aos/1176342476

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 4 • July, 1973
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