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Finite field models in additive combinatorics
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The study of many problems in additive combinatorics, such as Szemer\'edi's theorem on arithmetic progressions, is made easier by first studying models for the problem in 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.
Forward citations
Cited by 2 Pith papers
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Reasonable Bounds for Combinatorial Lines of Length Three
Any subset of {0,1,2}^n with density at least (log log log log n)^(-c) contains a combinatorial line of length 3.
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Algorithmic Polynomial Freiman-Ruzsa Theorems
Small-doubling subsets of F_2^n can now be covered by an explicit, efficiently learned subspace in polynomial time, with matching query lower bounds for classical and quantum algorithms.
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