A combinatorial structure of affine \((\alpha _1,\dots ,\alpha _t)\)-resolvable \((r,\lambda )\)-designs. (Q2716015)
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scientific article; zbMATH DE number 1600981
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A combinatorial structure of affine \((\alpha _1,\dots ,\alpha _t)\)-resolvable \((r,\lambda )\)-designs. |
scientific article; zbMATH DE number 1600981 |
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20 July 2005
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affine resolvability
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group divisible design
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0.8996244
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0.8981172
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0.8916366
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0.8905238
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0.8886614
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A combinatorial structure of affine \((\alpha _1,\dots ,\alpha _t)\)-resolvable \((r,\lambda )\)-designs. (English)
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An \((r,\lambda )\)-design is a BIB design with parameters \(v,b,r,k_j,j=1,\dots ,b\) such that every pair of treatments occurs exactly in \(\lambda \) blocks. Affine \((\alpha _1,\dots ,\alpha _t)\)-resolvability means that the \(b\) blocks are separated into \(t\) sets such that each set contains every treatment \(\alpha _l\) times and some more conditions are satisfied which we do not give here. The authors generalize some constructions of \textit{S.\ Kageyama} and \textit{D.\ V.\ S.\ Sastry} [Ars Comb.\ 36, 221-223 (1993; Zbl 0793.05014)] and prove a structural property of \(\alpha \)-resolvability to the effect that the existence of an affine \(\alpha \)-resolvable BIB design implies the existence of another one with certain different parameters.
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