Point-weight designs with design conditions on t points

This paper examines some of the properties of point-weight incidence structures, i.e. incidence structures for which every point is assigned a positive integer weight. In particular it examines point-weight designs with a design condition that stipulates that any two “identical” sets of t points must lie on the same number of blocks. We introduce a new class of designs with this property: row-sum designs, and examine the basic properties of row-sum point-weight designs and their similarities to classical (non-point-weight) designs and the point-weight designs of Horne [On point-weighted designs, Ph.D. Thesis, Royal Holloway, University of London, 1996].