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## GDDs with two associate classes and with three groups of sizes 1, n and n

Publisher(s)

Scopus

University of the Thai Chamber of Commerce

Date Issued

2014

Author(s)

Other Contributor(s)

University of the Thai Chamber of Commerce. Research Support Office

Abstract

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 differentgroups 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.

Subject(s)

Mathematics (General)

Access Rights

public

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.

Rights Holder(s)

University of the Thai Chamber of Commerce

Bibliographic Citation

W. Lapchinda, N. Punnim, P. Pabhapote (2014) GDDs with two associate classes and with three groups of sizes 1, n and n. Australasian Journal of Combinatorics Vol.58 No.2, 292-303.

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