Pairwise Balanced Designs with Block Sizes 8, 9, and 10
نویسندگان
چکیده
منابع مشابه
Pairwise balanced designs with block sizes 4 and 8
Let K be a set of positive integers. A pairwise balanced design (PBD) of index unity B(K,l;v) is a pair (X/~) where X is a v-set (of points) and B is a collection of subsets of X (called blocks) with sizes from K such that every pair of distinct points of X is contained in exactly one block of~. A necessary condition for the existence of a PBD B({4,8},I;v) is v-0 or l(mod 4). It is shown that t...
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The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that: λ(v − 1) ≡ 0 mod (k − 1) λv(v − 1) ≡ 0 mod k(k − 1) Earlier work has studied k = 9 with λ ∈ {1, 2, 3, 4, 6, 8, 9, 12}. In this article we show that the necessary conditions are sufficient for λ = 9 and every other λ not previously studied.
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In this paper, we are interested inminimizing the sum of block sizes in a pairwise balanced design, where there are some constraints on the size of one block or the size of the largest block. For every positive integers n,m, wherem ≤ n, letS (n,m) be the smallest integer s for which there exists a PBD on n points whose largest block has sizem and the sum of its block sizes is equal to s. Also, ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1997
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2742