## DIMACS TR: 98-34

## On the Dimension of the Hilbert-Cubes

### Author: Norbert Hegyvári

**
ABSTRACT
**

Let $A$ be a sequence of positive integers with positive density.
Then $A\cap\{1, 2, \ldots , n\}$ contains a Hilbert
(or combinatorial) cube of dimension $c\log\log n$.
We prove that this bound can not be replaced by $c'\sqrt{\log n\log\log n}$.

Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-34.ps.gz

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