##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics Seminar

## Dhruv Mubayi

#### University of Illinois, Chicago

## 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 C of all of them, and |C| is smaller than each of the sets. There has been a lot of recent progress on determining the maximum size of a sunflower-free family of subsets of [n]. We consider the problems of determining the maximum sum and product of k families of subsets of [n] that contain no sunflower of size k with one set from each family. We solve the sum problem exactly and make partial progress towards the product problem. \noindent{Joint work with Lujia Wang.}

Host: Andrew Suk and Jacques Verstraete

### February 27, 2018

### 3:00 PM

### AP&M 7321

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