The Sunflower-Free Process

An r-sunflower is a collection of r sets such that the intersection of any two sets in the collection is identical. We analyze a random process which constructs a w-uniform r-sunflower free family starting with an empty family and at each step adding a set chosen uniformly at random from all choices that could be added without creating an r-sunflower with the previously chosen sets. To analyze this process, we extend results of the first author and Bohman arXiv:1308.3732v5 [math.CO], who analyzed a general random process which adds one object at a time chosen uniformly at random from all objects that can be added without creating certain forbidden subsets.