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Finite field models in additive combinatorics. (English) Zbl 1155.11306
Webb, Bridget S. (ed.), Surveys in combinatorics 2005. Papers from the 20th British combinatorial conference, University of Durham, Durham, UK, July 10–15, 2005. Cambridge: Cambridge University Press (ISBN 0-521-61523-2/pbk). London Mathematical Society Lecture Note Series 327, 1-27 (2005).
Summary: The study of many problems in additive combinatorics, such as Szemerédi’s theorem on arithmetic progressions, is made easier by first studying models for the problem in $$\mathbb F_p^n$$ for some fixed small prime p. We give a number of examples of finite field models of this type, which allows us to introduce some of the central ideas in additive combinatorics relatively cleanly. We also give an indication of how the intuition gained from the study of finite field models can be helpful for addressing the original questions.
For the entire collection see [Zbl 1098.05002].

##### MSC:
 11B75 Other combinatorial number theory 05D05 Extremal set theory
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