##### Department of Mathematics,

University of California San Diego

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### Combinatorics Reading Seminar

## Jacques Verstraete

#### UCSD

## Product Representations of Polynomials

##### Abstract:

For a fixed polynomial $f \in \mathbb Z_k[X]$, let $\rho_k(N)$ denote the maximum size of a set $A \subset \{1,2,\dots,N\}$ such that no product of $k$ distinct elements of $A$ is in the value set of $f$. This problem was studied by Erd\H{o}s and Erd\H{o}s, S\'{o}s and S\'{a}rk\"{o}zy

### August 14, 2007

### 2:00 PM

### AP&M 7321

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