Ralph Gordon Stanton

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The quantity g (k) (v) was introduced in [6] as the minimum number of blocks necessary in a pairwise balanced design on v elements, subject to the condition that the longest block has length k. Recently, we have needed to use all possibilities for such minimal covering designs, and we record all non-isomorphic solutions to the problem for v ≤ 13.
This is a preprint of an article accepted for publication in the Ars Combina-toria c 2004 (copyright owner as specified in the journal). Abstract We survey the status of minimal coverings of pairs with block sizes two, three and four when λ = 1, that is, all pairs from a v-set are covered exactly once. Then we provide a complete solution for the case λ = 2.
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