On c -Bhaskar Rao Designs and tight embeddings for path designs

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 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 embeddin...

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Bibliographic Details
Published inDiscrete mathematics Vol. 308; no. 13; pp. 2659 - 2662
Main Authors Hurd, Spencer P., Sarvate, Dinesh G.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 06.07.2008
Subjects
[formula omitted]-Bhaskar Rao Design
[formula omitted]-BRD
BIBD
Handcuffed designs
Nested designs
Path design
Triple system
Nested designs
Path design
Triple system
BIBD
c -Bhaskar Rao Design
Handcuffed designs
c -BRD
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Summary: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 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.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2007.05.015