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arXiv · 1005.0155

On the size of dissociated bases

Vsevolod F. Lev·Raphael Yuster
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Abstract

We prove that the sizes of the maximal dissociated subsets of a given finite subset of an abelian group differ by a logarithmic factor at most. On the other hand, we show that the set $\{0,1\}^n\seq\Z^n$ possesses a dissociated subset of size $\Ome(n\log n)$; since the standard basis of $\Z^n$ is a maximal dissociated subset of $\{0,1\}^n$ of size $n$, the result just mentioned is essentially sharp.

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Vsevolod F. Lev, Raphael Yuster. 2010-05-02. On the size of dissociated bases. https://arxiv.org/abs/1005.0155

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