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|Title:||Group divisible designs with two associate classes and λ1 λ2 = 1||Authors:||Lapchinda, W.
University of the Thai Chamber of Commerce
|Source:||W. Lapchinda, N. Pabhapote (2010) Group divisible designs with two associate classes and λ1 λ2 = 1. International Journal of Pure and Applied Mathematics Vol.54 No.4, 601-608.||Abstract:||A group divisible design GDD(v, g, k, λ1, λ2) is a collection of ksubsets (called blocks) of a vsetof symbols where: the vset is divided into g groups; each pair of symbols from the same group occurs in exactly λ1 blocks; and each pair symbols from different groups occurs in exactly λ2 blocks. Pairs of symbols occurring in the same group are known to statisticians as firstassociates, and pairs occurring in different groups are called second associates. The existence of such GDDs has been of interest over the years, going back to at least the work of Bose and Shimamoto in 1952 who began classifying such designs. Recently, such an existence problem when g = 2 was solved in the case where the groups have the same size and the blocks have size 3. In this paper, we continue to focus on blocks of size 3, solving the problem when the required designs having twogroups of unequal sizes and λ1 λ2 = 1 and prove that the conditions are sufficient.||URI:||https://scholar.utcc.ac.th/handle/6626976254/3622||Rights:||This work is protected by copyright. Reproduction or distribution of the work in any format is prohibited without written permission of the copyright owner.|
|Appears in Collections:||RSO: Journal Articles|
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