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- W1977424721 abstract "In this paper we observe that in the hypergraph removal lemma, the edge removal can be done in such a way that the symmetries of the original hypergraph remain preserved. As an application we prove the following generalization of Szemerédiâs Theorem on arithmetic progressions. Let $A$ be an Abelian group with subsets $S_1,S_2,dots ,S_t$ such that the number of arithmetic progressions $x,x+d,dots ,x+(t-1)d$ with $x+(i-1)din S_i$ is $o(|A|^2)$. Then we can shrink each $S_i$ by $o(|A|)$ elements such that the new sets donât have any arithmetic progression of the above type." @default.
- W1977424721 created "2016-06-24" @default.
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- W1977424721 date "2009-10-14" @default.
- W1977424721 modified "2023-09-28" @default.
- W1977424721 title "The symmetry preserving removal lemma" @default.
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- W1977424721 doi "https://doi.org/10.1090/s0002-9939-09-09860-8" @default.
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