Speaker
Description
The concept of higher-dimensional combinatorial designs was introduced by Warwick de Launey in 1990. Recently we have studied higher-dimensional incidence structures. Since symmetric designs have the same number of points and blocks, their incidence matrices can easily be superposed to get a 3- or higher-dimensional binary cube. We have focused on 3-dimensional cubes of symmetric $(v,k,\lambda)$ designs, hence 3-dimensional binary matrices of order $v$. They show to be equivalent to $(v,k,\lambda)$ difference sets by an easy-to-follow construction. Therefore, we tried and succeeded to manage to construct examples where the cube does not come from a difference set in this straightforward way. In addition, we have been successful in constructing cubes for which the 2-dimensional slices are incidence matrices of non-isomorphic designs. In this talk we will provide constructive examples and open questions on this topic.
