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

Mathematics

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 (US)
Article number	3
Journal	Discrete Analysis
Volume	2019
DOIs	https://doi.org/10.19086/da.7757
State	Published - 2019

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

Keywords

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

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10.19086/da.7757

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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.",

keywords = "Arithmetic regularity, Induced patterns, Property testing, Regularity lemma, Removal lemma, Vc dimension",

author = "Noga Alon and Jacob Fox and Yufei Zhao",

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journal = "Discrete Analysis",

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AU - Alon, Noga

AU - Fox, Jacob

AU - Zhao, Yufei

N1 - Publisher Copyright: © Licensed under a Creative Commons Attribution License (CC-BY)

PY - 2019

Y1 - 2019

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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VL - 2019

JO - Discrete Analysis

JF - Discrete Analysis

M1 - 3

ER -

Efficient Arithmetic Regularity and Removal Lemmas for Induced Bipartite Patterns

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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