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Title: GDDs with two associate classes and with three groups of sizes 1, n, n and λ1 &t; λ2
Authors: Lapchinda, W. 
Punnim, N. 
Pabhapote, N. 
Issue Date: 2013
Publisher: Scopus
University of the Thai Chamber of Commerce
Source: W. Lapchinda, N. Punnim, N. Pabhapote (2013) GDDs with two associate classes and with three groups of sizes 1, n, n and λ1 &t; λ2. Lecture Notes in Computer Science, 101-109.
Abstract: A group divisible design GDD(v = 1 + n + n, 3, 3, λ1, λ2) is an ordered pair (V, B) where V is an (1 + n + n)setof symbols and B is a collection of 3subsets(called blocks) of V satisfying the following properties: the (1 + n + n)set is divided into 3 groups of sizes 1, n and n; each pair of symbols from the same group occurs in exactly λ1 blocks in B; and each pair of symbols fromdifferent groups occurs in exactly λ2 blocks in B. Let λ1, λ2 be positive integers. Then the spectrum of λ1, λ2, denoted by Spec(λ1, λ2), is defined by Spec(λ1, λ2) = {n ∈ ℕ : a GDD(v = 1 + n + n, 3, 3, λ1, λ2) exists}. We found in [10] the spectrum Spec(λ1, λ2) provided that λ1 ≥ λ2 in all situations. We find in this paper Spec(λ1, λ2) when λ1 &t; λ2 in all situations.
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.
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