منابع مشابه
Thickly-resolvable block designs
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, ...
متن کاملResolvable Designs with Large Blocks
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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Amongst resolvable incomplete block designs, affine resolvable designs are optimal in many conventional senses. However, different affine resolvable designs for the same numbers of treatments, replicates, and block size can differ in how well they estimate elementary treatment contrasts. An aberration criterion is employed to distinguish the best of the affine resolvable designs for this task. ...
متن کاملDoubly 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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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1985
ISSN: 0097-3165
DOI: 10.1016/0097-3165(85)90033-0