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math.COApr 8, 2014
13
citations (OpenAlex)
authors
  • Tomasz Schoen
  • Ilya D. Shkredov
institutions
  • Adam Mickiewicz University in Poznań
  • Institute for Information Transmission Problems
  • Steklov Mathematical Institute
  • Yaroslavl State University
arXiv abstractPDF
paper

Additive dimension and a theorem of Sanders

arXiv:1404.2044 · doi:10.1017/S1446788715000324

Abstract

We prove some new bounds for the size of the maximal dissociated subset of structured (having small sumset, large energy and so on) subsets A of an abelian group.

20 pages

References in corpus (9)

  • On the Bogolyubov-Ruzsa lemma
  • On Roth's theorem on progressions
  • The structure theory of set addition revisited
  • An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm
  • On certain other sets of integers
  • Structure in additively nonsmoothing sets
  • On sets with small doubling
  • On a theorem of Shkredov
  • Structure in sets with logarithmic doubling

Cited by in corpus (3)

  • Additive Combinatorics: A Menu of Research Problems
  • New Upper Bound for Sums of Dilates
  • On the dimension of additive sets
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