IJPAM: Volume 104, No. 1 (2015)
GROUP DIVISIBLE DESIGNS
Department of Mathematics and Computer Science
Faculty of Science
Payathai Rd., Bangkok 10330, THAILAND
Department of Mathematics
Sukhumvit 23, Bangkok 10110, THAILAND
Abstract. A group divisible design is an ordered pair where is an -set of symbols and is a collection of -subsets (called blocks) of satisfying the following properties: the -set is divided into two groups of size and ; each pair of symbols from the same group occurs in exactly one block in ; and each pair of symbols from different groups occurs in exactly three blocks in . Given positive integers and , two necessary conditions on and for the existence of a are and . We show that these conditions are sufficient for the most cases.
Received: March 23, 2015
AMS Subject Classification:
Key Words and Phrases: group divisible design, difference triple, graph decomposition
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DOI: 10.12732/ijpam.v104i1.2 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 19 - 28
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