Additive combinatorics and graph theory

  • Endre Szemerédi

    Hungarian Academy of Sciences, Budapest, Hungary
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In this survey we mainly discuss the conditions for a set to contain long arithmetic progressions. We mention the ergodic, Fourier analytic and combinatorial approach to provide such conditions. In addition we describe defferent graph theoretic results with various applications in additive combinatorics and computer science. Finally, we mention some elementary results in discrete geometry.