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Lapchinda, W. and Punnim, N. and Pabhapote, P. (2014) GDDs with two associate classes and with three groups of sizes 1, n and n. Australasian Journal of Combinatorics, 58 (2). pp. 292-303.


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A group divisible design GDD(v = 1+n+ n, 3, λ1, λ2) is an ordered pair (V, B) where V is an (1 + n + n)set of 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 from different groups occurs in exactly λ2 blocks in B. 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, λ1, λ2) exists}. We find the spectrum Spec(λ1, λ2) for all λ1 ≥ λ2.

Item Type: Article
Subjects: Science and Technology > Mathematics (General)
Divisions: Research Center > Research Support Office
Depositing User: Miss Niramol Sudkhanung
Date Deposited: 17 Jun 2016 08:42
Last Modified: 17 Jun 2016 08:42
URI: http://eprints.utcc.ac.th/id/eprint/5640

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