Please use this identifier to cite or link to this item:
https://ir.swu.ac.th/jspui/handle/123456789/14290
Title: | Group divisible designs with two associate classes and (λ 1, λ 2) = (1, 2) |
Authors: | Purmim N. Uiyyasathian C. |
Keywords: | Construction technique Group divisible design Sufficient conditions Combinatorial mathematics Mathematical techniques |
Issue Date: | 2012 |
Abstract: | A group divisible design GDD(v = v 1 + v 2 + -+v g, g, k; λ 1, λ 2) is an ordered pair (V, B) where V is a v-set of symbols and B is a collection of k-subsets (called blocks) of V satisfying the following properties: the v-set is divided into g groups of sizes v 1, v 2,...,V g; each pair of symbols from the same group occurs in exactly λ 1 blocks in B; and each pair of symbols from different groups occurs in exactly λ 2 blocks in B. In this paper we give necessary conditions on m and n for the existence of a GDD(v = m + n, 2, 3; 1, 2), along with sufficient conditions for each m ≤ n/2. Furthermore, we introduce some construction techniques to construct some GDD(v = m + n, 2, 3, l, 2)s when m>%n/2, namely, a GDD(v = 9+15, 2, 3; 1, 2) and a GDD(v = 25 + 33, 2, 3; 1, 2). |
URI: | https://ir.swu.ac.th/jspui/handle/123456789/14290 https://www.scopus.com/inward/record.uri?eid=2-s2.0-84864856815&partnerID=40&md5=eff63377f3e473236247b957f021ef26 |
ISSN: | 8353026 |
Appears in Collections: | Scopus 1983-2021 |
Files in This Item:
There are no files associated with this item.
Items in SWU repository are protected by copyright, with all rights reserved, unless otherwise indicated.