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## GDDs with two associate classes and with three groups of sizes 1, n, n and λ1 &t; λ2

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University of the Thai Chamber of Commerce. Research Support Office

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Scopus

University of the Thai Chamber of Commerce

Date Issued

2013

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Journal article

Language

English

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.

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University of the Thai Chamber of Commerce

Bibliographic Citation

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.