منابع مشابه
Doubly resolvable designs with small parameters
Doubly resolvable 2-(v,k,λ) designs (DRDs) with small parameters and their resolutions which have orthogonal resolutions (RORs) are constructed and classified up to isomorphism. Exact values or lower bounds on the number of the nonisomorphic sets of m mutually orthogonal resolutions (m-MORs) are presented. The implemented algorithms and the parameter range of this method are discussed, and the ...
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We show that the necessary divisibility conditions for the existence of a σ-resolvable BIBD(v, k, λ) are sufficient for large v. The key idea is to form an auxiliary graph based on an [r, k]-configuration with r = σ, and then edge-decompose the complete λ-fold graph K (λ) v into this graph. As a consequence, we initiate a similar existence theory for incomplete designs with index λ. ∗ Supported...
متن کاملSome Block Designs Constructed from Resolvable Designs
LetD be a resolvable 2−(v, k, λ) design, andD′ be a 2−(v′, k′, λ′) design, such that v′ = v k . Further, let r and r′ be replication numbers of a point in D and D′, respectively. Shrikhande and Raghavarao proved that then there exists a 2 − (v′′, k′′, λ′′) design D′′, such that v′′ = v, k′′ = kk′ and λ′′ = r′λ + (r − λ)λ′. If D′ is resolvable, then D′′ is also resolvable. Applying this result, ...
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An m-cycle system C of λKn is said to be near resolvable if the mcycles in C can be partitioned into near parallel classes R1, R2, . . . , Rλn/2, each one of which is a 2-factor of λKn − v for some vertex v in λKn. If an NR(n,m, λ)-CS has a pair of orthogonal resolutions, it is said to be doubly resolvable and is denoted by DNR(n,m, λ)-CS. For m = 2, 3, DNR(n,m, 2)-CSs are known as Room frames ...
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Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information matrix, and consequently in terms of block concurrences. Equalizing block concurrences for given block sizes is often, but not always, the best strategy. Su...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1980
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90288-s