##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Van Vu

#### UCSD

## Long arithmetic progressions in sumsets and the number of zero-sum-free sets

##### Abstract:

Let n be a large prime. A set A of residues modulo n is zero-sum-free if no subsetsum of A is divisible by n. Zero-sum-free sets have been studied for a long time but little was know about the following fundamental question: How many zero-sum-free sets are there ?In this talk, we shall present a sharp answer to this question, using new results about long arithmetic progressions in sumsets. In fact, we are able to characterize zero-sum-free sets: the main (and natural) reason for a set to be zero-sum-free is that the sum of its elements is less than n. (joint work with E. Szemeredi)

Host:

### March 4, 2003

### 3:00 PM

### AP&M 7321

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