Graduate Combinatorics Seminar
Lujia Wang
UIC
Multicolor Sunflowers
Abstract: A sunflower is a collection of distinct sets such that the intersection of any two of them is the same as the common intersection of all of them. A longstanding conjecture due to Erdös and Szemerédi states that the maximum size of a family of subsets of $[n]$ that contains no sunflower of size $k>2$ is exponentially smaller than $2^n$. We consider this problem for multiple families. In particular, we obtain sharp or almost sharp bounds on the sum and product of $k$ families of subsets of $[n]$ that together contain no sunflower of size $k$ with one set from each family. This is joint work with Dhruv Mubayi.
Wednesday March 4, 2015 at 4:00 PM in SEO 712