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...
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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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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. ...
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In this paper we describe a backtrack search over parallel classes with a partial isomorph rejection to classify resolvable 2-(12, 6, 5c) designs. We use the intersection pattern between the parallel classes and the fact that any resolvable 2-(12, 6, 5c) design is also a resolvable 3-(12, 6, 2c) design to effectively guide the search. The method was able to enumerate all nonsimple resolutions a...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1972
ISSN: 0012-365X
DOI: 10.1016/0012-365x(72)90091-x