Efficient Arithmetic Regularity and Removal Lemmas for Induced Bipartite Patterns

Noga Alon; Jacob Fox; Yufei Zhao

doi:10.19086/da.7757

Efficient Arithmetic Regularity and Removal Lemmas for Induced Bipartite Patterns

Noga Alon
, Jacob Fox
, Yufei Zhao

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Let G be an abelian group of bounded exponent and A ⊆ 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 ejGj elements to/from A to make it a union of H-cosets.

Original language	English
Article number	3
Journal	Discrete Analysis
Volume	2019
DOIs	https://doi.org/10.19086/da.7757
State	Published - 1 Jan 2019
Externally published	Yes

Keywords

Arithmetic regularity
Induced patterns
Property testing
Regularity lemma
Removal lemma
Vc dimension

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

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abstract = "Let G be an abelian group of bounded exponent and A ⊆ 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 ejGj elements to/from A to make it a union of H-cosets.",

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AU - Zhao, Yufei

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Y1 - 2019/1/1

N2 - Let G be an abelian group of bounded exponent and A ⊆ 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 ejGj elements to/from A to make it a union of H-cosets.

AB - Let G be an abelian group of bounded exponent and A ⊆ 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 ejGj elements to/from A to make it a union of H-cosets.

KW - Arithmetic regularity

KW - Induced patterns

KW - Property testing

KW - Regularity lemma

KW - Removal lemma

KW - Vc dimension

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JO - Discrete Analysis

JF - Discrete Analysis

M1 - 3

ER -

Efficient Arithmetic Regularity and Removal Lemmas for Induced Bipartite Patterns

Abstract

Keywords

ASJC Scopus subject areas

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