On the structure of sum-free sets, 2

Jean Marc Deshouillers; Gregory A. Freiman; Vera Sós; Mikhail Temkin

On the structure of sum-free sets, 2

Jean Marc Deshouillers^*
, Gregory A. Freiman
, Vera Sós
, Mikhail Temkin

^*Corresponding author for this work

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

25 Scopus citations

Abstract

A finite set of positive integers is called sum-free if double-struck A∩n (double-struck A + double-struck A) is empty, where double-struck A + double-struck A denotes the set of sums of pairs of non necessarily distinct elements from double-struck A. Improving upon a previous result by G.A. Freiman, a precise description of the structure of sum-free sets included in [1, M] with cardinality larger than 0.4M - x for M ≥ M₀(x) (where x is an arbitrary given number) is given.

Original language	English
Pages (from-to)	149-161
Number of pages	13
Journal	Asterisque
Volume	258
State	Published - 1999
Externally published	Yes

Keywords

Additive number theory
Arithmetic progressions
Combinatorial number theory
Sum-free sets

Cite this

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abstract = "A finite set of positive integers is called sum-free if double-struck A∩n (double-struck A + double-struck A) is empty, where double-struck A + double-struck A denotes the set of sums of pairs of non necessarily distinct elements from double-struck A. Improving upon a previous result by G.A. Freiman, a precise description of the structure of sum-free sets included in [1, M] with cardinality larger than 0.4M - x for M ≥ M0(x) (where x is an arbitrary given number) is given.",

keywords = "Additive number theory, Arithmetic progressions, Combinatorial number theory, Sum-free sets",

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year = "1999",

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AU - Deshouillers, Jean Marc

AU - Freiman, Gregory A.

AU - Sós, Vera

AU - Temkin, Mikhail

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AB - A finite set of positive integers is called sum-free if double-struck A∩n (double-struck A + double-struck A) is empty, where double-struck A + double-struck A denotes the set of sums of pairs of non necessarily distinct elements from double-struck A. Improving upon a previous result by G.A. Freiman, a precise description of the structure of sum-free sets included in [1, M] with cardinality larger than 0.4M - x for M ≥ M0(x) (where x is an arbitrary given number) is given.

KW - Additive number theory

KW - Arithmetic progressions

KW - Combinatorial number theory

KW - Sum-free sets

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JO - Asterisque

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ER -

On the structure of sum-free sets, 2

Abstract

Keywords

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