On c -Bhaskar Rao Designs and tight embeddings for path designs
- 作者：Spencer P. Hurd ; Dinesh G. Sarvate
- 关键词：BIBD ; none ; color ; black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V00-4NWCH18-K&_mathId=mml11&_user=1067359&_cdi=5632&_rdoc=4&_acct=C000050221&_version=1&_userid=10&md5=84cd607993f4b98b66bff9d9cba359
- 刊名：Discrete Mathematics
- 出版年：2008
- 期刊代码：47_0012365x
- 类别：cp
- 出版时间：6 July 2008
- 卷：308
- 期：13
- 页码：2659-2662
- 文件大小：121 K
摘要
Under the right conditions it is possible for the ordered blocks of a path design PATH(v,k,μ) to be considered as unordered blocks and thereby create a 20d19d344b11" title="Click to view the MathML source" alt="Click to view the MathML source">BIBD(v,k,λ). We call this a tight embedding. We show here that, for any triple system TS(v,3), there is always such an embedding and that the problem is equivalent to the existence of a (-1)-BRD(v,3,3), i.e., a c-Bhaskar Rao Design. That is, we also prove the incidence matrix of any triple system TS(v,3) can always be signed to create a (-1)-BRD(v,3,3) and, moreover, the signing determines a natural partition of the blocks of the triple system making it a nested design.