The number of repeated blocks in twofold triple systems
The number of repeated blocks in twofold triple systems
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DOI：
10.1016/0097-3165(86)90115-9
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发表时间：
1986
期刊：
影响因子：
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通讯作者：
A. Rosa;D. Hoffman
中科院分区：
文献类型：
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作者：
A. Rosa;D. Hoffman
In this paper, we give a complete answer to the following question: Given an integer υ≡ 0 or 1 (mod 3) and an integer k, does there exist a twofold triple system of order υ with exactly k repeated triples? In particular, we prove the following theorem: If υ≡ 0 or 4 (mod 6), υ> 12, then there exists a twofold triple system of order υ having exactly k repeated triples if and only if k ϵ I′ υ, where I′ υ={0, 1,…, s υ− 2, s υ} if υ≡ 0 (mod 4), I′ υ={0, 1,…, s υ− 1} if υ≡ 2 (mod 4), and s υ= υ (υ− 4) 6.
