Iterated compositions of linear operations on sets of positive upper density

Norbert Hegyvári; François Hennecart; Alain Plagne

doi:10.1142/S179304210900250X

Iterated compositions of linear operations on sets of positive upper density

Norbert Hegyvári
, François Hennecart
, Alain Plagne

Eötvös Loránd University
Université Jean Monnet Saint-Étienne

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

Abstract

Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded coefficients) on sets of integers having a positive upper density.

Original language	English
Pages (from-to)	981-997
Number of pages	17
Journal	International Journal of Number Theory
Volume	5
Issue number	6
DOIs	https://doi.org/10.1142/S179304210900250X
Publication status	Published - 1 Jan 2009

Keywords

Difference set
Gaps
Linear operation
Periodicity
Stability
Structure
Upper density

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title = "Iterated compositions of linear operations on sets of positive upper density",

abstract = "Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded coefficients) on sets of integers having a positive upper density.",

keywords = "Difference set, Gaps, Linear operation, Periodicity, Stability, Structure, Upper density",

author = "Norbert Hegyv{\'a}ri and Fran{\c c}ois Hennecart and Alain Plagne",

year = "2009",

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AU - Hennecart, François

AU - Plagne, Alain

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N2 - Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded coefficients) on sets of integers having a positive upper density.

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KW - Difference set

KW - Gaps

KW - Linear operation

KW - Periodicity

KW - Stability

KW - Structure

KW - Upper density

UR - https://www.scopus.com/pages/publications/70350075941

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DO - 10.1142/S179304210900250X

M3 - Article

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SP - 981

EP - 997

JO - International Journal of Number Theory

JF - International Journal of Number Theory

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ER -

Iterated compositions of linear operations on sets of positive upper density

Abstract

Keywords

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