On the size of dissociated bases

Vsevolod F. Lev; Raphael Yuster

doi:10.37236/604

On the size of dissociated bases

Vsevolod F. Lev, Raphael Yuster

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 ⊆ Zⁿ possesses a dissociated subset of size Ω(n log n); since the standard basis of Zⁿ is a maximal dissociated subset of {0, 1}ⁿ of size n, the result just mentioned is essentially sharp.

Original language	English
Pages (from-to)	1-5
Number of pages	5
Journal	Electronic Journal of Combinatorics
Volume	18
Issue number	1
DOIs	https://doi.org/10.37236/604
State	Published - 2011

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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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 ⊆ Zn possesses a dissociated subset of size Ω(n log n); since the standard basis of Zn is a maximal dissociated subset of {0, 1}n of size n, the result just mentioned is essentially sharp.",

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AB - 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 ⊆ Zn possesses a dissociated subset of size Ω(n log n); since the standard basis of Zn is a maximal dissociated subset of {0, 1}n of size n, the result just mentioned is essentially sharp.

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On the size of dissociated bases

Abstract

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