Ergodic Methods in Additive Combinatorics

  title={Ergodic Methods in Additive Combinatorics},
  author={Bryna Kra},
  journal={arXiv: Dynamical Systems},
  • Bryna Kra
  • Published 3 August 2006
  • Mathematics
  • arXiv: Dynamical Systems
Shortly after Szemer\'edi's proof that a set of positive upper density contains arbitrarily long arithmetic progressions, Furstenberg gave a new proof of this theorem using ergodic theory. This gave rise to the field of ergodic Ramsey Theory, in which problems motivated by additive combinatorics are proven using ergodic theory. Ergodic Ramsey Theory has since produced combinatorial results, some of which have yet to be obtained by other means, and has also given a deeper understanding of the… 

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