On image-Bhaskar Rao Designs and tight embeddings for path designs Original Research Article

Under the right conditions it is possible for the ordered blocks of a path design image to be considered as unordered blocks and thereby create a image. We call this a tight embedding. We show here that, for any triple system image, there is always such an embedding and that the problem is equivalent to the existence of a image, i.e., a image-Bhaskar Rao Design. That is, we also prove the incidence matrix of any triple system image can always be signed to create a image and, moreover, the signing determines a natural partition of the blocks of the triple system making it a nested design.