A Szemerédi-type regularity lemma in abelian groups
نویسنده
چکیده
Szemerédi’s regularity lemma is an important tool in graph theory which has applications throughout combinatorics. In this paper we prove an analogue of Szemerédi’s regularity lemma in the context of abelian groups and use it to derive some results in additive number theory. The simplest is a structure theorm for sets which are almost sum-free. If A ⊆ {1, . . . , N} has δN2 triples (a1, a2, a3) for which a1+a2 = a3 then A = B∪C, where B is sum-free and |C| = δ′N , and δ′ → 0 as δ → 0.
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