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. Our bound shows that there is a constant α such that any family of $(\alpha p \log(pk))^k$ sets of size $k$ must contain a $p$-sunflower.

combinatoricsmetric geometry

Audience: researchers in the topic

UW combinatorics and geometry seminar