On the size of dissociated bases

Vsevolod F. Lev, Raphael Yuster

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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 ⊆ 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 languageEnglish
Pages (from-to)1-5
Number of pages5
JournalElectronic Journal of Combinatorics
Issue number1
StatePublished - 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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