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Efficient arithmetic regularity and removal lemmas for induced bipartite patterns
Discrete analysis (2019) Cet article a éte moissonné depuis la source Scholastica

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Let $G$ be an abelian group of bounded exponent and $A \subseteq G$. We show that if the collection of translates of $A$ has VC dimension at most $d$, then for every $ε>0$ there is a subgroup $H$ of $G$ of index at most $ε^{-d-o(1)}$ such that one can add or delete at most $ε|G|$ elements to/from $A$ to make it a union of $H$-cosets. We also establish a removal lemma with polynomial bounds, with applications to property testing, for induced bipartite patterns in a finite abelian group with bounded exponent.
Publié le : 
@article{DAS_2019_a17,
     author = {Noga Alon and Jacob Fox and Yufei Zhao},
     title = {Efficient arithmetic regularity and removal lemmas for induced bipartite patterns},
     journal = {Discrete analysis},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2019_a17/}
}
TY  - JOUR
AU  - Noga Alon
AU  - Jacob Fox
AU  - Yufei Zhao
TI  - Efficient arithmetic regularity and removal lemmas for induced bipartite patterns
JO  - Discrete analysis
PY  - 2019
UR  - http://geodesic.mathdoc.fr/item/DAS_2019_a17/
LA  - en
ID  - DAS_2019_a17
ER  - 
%0 Journal Article
%A Noga Alon
%A Jacob Fox
%A Yufei Zhao
%T Efficient arithmetic regularity and removal lemmas for induced bipartite patterns
%J Discrete analysis
%D 2019
%U http://geodesic.mathdoc.fr/item/DAS_2019_a17/
%G en
%F DAS_2019_a17
Noga Alon; Jacob Fox; Yufei Zhao. Efficient arithmetic regularity and removal lemmas for induced bipartite patterns. Discrete analysis (2019). http://geodesic.mathdoc.fr/item/DAS_2019_a17/