Induced arithmetic removal: complexity 1 patterns over finite fields

Jacob Fox; Jonathan Tidor; Yufei Zhao

doi:10.1007/s11856-022-2290-x

Induced arithmetic removal: complexity 1 patterns over finite fields

Jacob Fox
, Jonathan Tidor
, Yufei Zhao

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

2 Scopus citations

Abstract

We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that given a fixed collection of r-colored complexity 1 arithmetic patterns over F_q, every coloring ϕ:Fqn\{0}→[r] with o(1) density of every such pattern can be recolored on an o(1)-fraction of the space so that no such pattern remains.

Original language	English (US)
Pages (from-to)	1-38
Number of pages	38
Journal	Israel Journal of Mathematics
Volume	248
Issue number	1
DOIs	https://doi.org/10.1007/s11856-022-2290-x
State	Published - May 2022
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/s11856-022-2290-x

Cite this

@article{f842438837a247d4960f593b1c525288,

title = "Induced arithmetic removal: complexity 1 patterns over finite fields",

abstract = "We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that given a fixed collection of r-colored complexity 1 arithmetic patterns over Fq, every coloring ϕ:Fqn\textbackslash{}\{0\}→[r] with o(1) density of every such pattern can be recolored on an o(1)-fraction of the space so that no such pattern remains.",

author = "Jacob Fox and Jonathan Tidor and Yufei Zhao",

note = "Publisher Copyright: {\textcopyright} 2022, The Hebrew University of Jerusalem.",

year = "2022",

month = may,

doi = "10.1007/s11856-022-2290-x",

language = "English (US)",

volume = "248",

pages = "1--38",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Induced arithmetic removal

T2 - complexity 1 patterns over finite fields

AU - Fox, Jacob

AU - Tidor, Jonathan

AU - Zhao, Yufei

PY - 2022/5

Y1 - 2022/5

N2 - We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that given a fixed collection of r-colored complexity 1 arithmetic patterns over Fq, every coloring ϕ:Fqn\{0}→[r] with o(1) density of every such pattern can be recolored on an o(1)-fraction of the space so that no such pattern remains.

AB - We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that given a fixed collection of r-colored complexity 1 arithmetic patterns over Fq, every coloring ϕ:Fqn\{0}→[r] with o(1) density of every such pattern can be recolored on an o(1)-fraction of the space so that no such pattern remains.

UR - https://www.scopus.com/pages/publications/85125778851

UR - https://www.scopus.com/pages/publications/85125778851#tab=citedBy

U2 - 10.1007/s11856-022-2290-x

DO - 10.1007/s11856-022-2290-x

M3 - Article

AN - SCOPUS:85125778851

SN - 0021-2172

VL - 248

SP - 1

EP - 38

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -

Induced arithmetic removal: complexity 1 patterns over finite fields

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this