Geodesic
On the size of dissociated bases
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/604
Classification : 05B10, 11B13, 05D40 
@article{10_37236_604,
     author = {Vsevolod F. Lev and Raphael Yuster},
     title = {On the size of dissociated bases},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/604},
     zbl = {1217.05046},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/604/}
}
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Vsevolod F. Lev; Raphael Yuster. On the size of dissociated bases. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/604

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