Publication: GDDs with two associate classes and with three groups of sizes 1, n, n and λ1 < λ2
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Issued Date
2013
Resource Type
File Type
application/pdf
ISSN
3029743
Other identifier(s)
2-s2.0-84891844902
Rights Holder(s)
มหาวิทยาลัยศรีนครินทรวิโรฒ
Bibliographic Citation
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol 8296 LNCS, (2013), p.101-109
Suggested Citation
Lapchinda W., Punnim N., Pabhapote N. GDDs with two associate classes and with three groups of sizes 1, n, n and λ1 < λ2. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol 8296 LNCS, (2013), p.101-109. doi:10.1007/978-3-642-45281-9_10 Retrieved from: https://hdl.handle.net/20.500.14740/6497
Author(s)
Abstract
A group divisible design GDD(v = 1 + n + n, 3, 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 3-subsets (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. Let λ1, λ2 be positive integers. Then the spectrum of λ1, λ2, denoted by Spec(λ 1, λ2), is defined by Spec(λ1, λ2) = {n ∈ ℕ : a GDD(v = 1 + n + n, 3, 3, λ1, λ2) exists}. We found in [10] the spectrum Spec(λ1, λ2) provided that λ1 ≥ λ2 in all situations. We find in this paper Spec(λ1, λ2) when λ1 < λ2 in all situations. © 2013 Springer-Verlag.