# On the Size of Dissociated Bases

@article{Lev2011OnTS,
title={On the Size of Dissociated Bases},
author={Vsevolod F. Lev and Raphael Yuster},
journal={Electron. J. Comb.},
year={2011},
volume={18}
}
• Published 2 May 2010
• Mathematics
• Electron. J. Comb.
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 $\{0,1\}^n\subseteq\mathbb{Z}^n$ possesses a dissociated subset of size $\Omega(n\log n)$; since the standard basis of $\mathbb{Z}^n$ is a maximal dissociated subset of $\{0,1\}^n$ of size $n$, the result just mentioned is essentially sharp.
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