Constructions and bounds for image-splitting systems Original Research Article

Let m and t be positive integers with image. An image-splitting system is a pair image where image and image is a collection of subsets of X called blocks such that for every image with image, there exists a block image such that image. An image-splitting system is uniform if every block has size image. In this paper, we give several constructions and bounds for splitting systems, concentrating mainly on the case image. We consider uniform splitting systems as well as other splitting systems with special properties, including disjunct and regular splitting systems. Some of these systems have interesting connections with other types of set systems.