Coding for Sunflowers

Abstract

A sunflower is a family of sets that have the same pairwise intersections. We simplify a recent result of Alweiss, Lovett, Wu and Zhang that gives an upper bound on the size of every family of sets of size k that does not contain a sunflower. We show how to use the converse of Shannon’s noiseless coding theorem to give a cleaner proof of a similar bound.