FoCM 2014 conference

Plenary talk

December 11, 9:30 ~ 10:25

## On subset sums

### Endre Szemeredi

### Hungarian Academy of Science and Rutgers University , Hungary and USA - szemered@cs.rutgers.edu

Let $A \subset [1;N]$ be a set of integers. We denote by $S_A$ the collection of partial sums of $A$,

$$S_A =\left\{ \sum_{x\in B} x: B\subset A\right\}.$$

For a positive integer $l \le A$ we denote by $l^*A$ the collection of partial sums of $l$ elements of $A$,

$$l^*A =\left\{ \sum_{x\in B} x: B\subset A, |B|=l\right\}.$$

We will discuss the structure of $l^*A$ and give a tight bound of the size of $A$ not containing an $N$ element arithmetic progression.

Some of the results are joint with Van Vu, the others are joint work with Simao Herdade.

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