IJPAM: Volume 104, No. 1 (2015)
GROUP DIVISIBLE DESIGNS




Faculty of Science
Chulalongkorn University
Payathai Rd., Bangkok 10330, THAILAND

Srinakharinwirot University
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
Year: 2015
Volume: 104
Issue: 1
Pages: 19 - 28
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