A construction of group divisible designs |
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Authors: | Dieter Jungnickel |
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Affiliation: | 2. Mathematisches Institut der Freien Universität Berlin, Königin-Luise-Str. 24/26, D-1000 Berlin 33, F.R.Germany |
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Abstract: | Given any affine design with parameters v, b, r, k, λ and μ = k2/v and any design with parameters v′, b′, r′, k′, λ′ where r′ = tr for some natural number `t and k′?r, we construct a group divisible design with parameters v′' = vv′, m = v′, n = v, b′' = vb′, k′' = kk′, r′'= kr′, λ1 = tkλ and λ2 = μλ′. This is applied to some series of designs. As a lemma, we also show that any 0-1-matrix with row sums tr and column sums ?r may be written as the sum of r 0-1-matrices with row sums t and column sums ?1. |
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Keywords: | 05 B 25 05 B 05 Auxillary Matrices Group Divisible Design Affine Design König's Lemma 0-1-matrices |
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