On set systems with a threshold property Original Research Article

For image and t such that image, a set image of subsets of image has the image-threshold property if every k-subset of image contains at least t sets from image and every image-subset of image contains less than t sets from image. The minimal number of sets in a set system with this property is denoted by image. In this paper we determine image exactly for n sufficiently large, and we show that image is asymptotically equal to the generalized Turán number image.