On small sumsets in (ℤ/2ℤ)n

Jean Marc Deshouillers; François Hennecart; Alain Plagne

doi:10.1007/s00493-004-0004-0

On small sumsets in (ℤ/2ℤ)ⁿ

Jean Marc Deshouillers
, François Hennecart
, Alain Plagne

IMB UMR 5251
Université Jean Monnet Saint-Étienne

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

Abstract

It is proved that any subset A of (ℤ/2ℤ)ⁿ, having k elements, such that |A+A|=c|A| (with c<4), is contained in a subgroup of order at most u^-1k where u = u(c) > 0 is an explicit function of c which does not depend on k nor on n. This improves by a radically different method the corresponding bounds deduced from a more general result of I. Z. Ruzsa.

Original language	English
Pages (from-to)	53-68
Number of pages	16
Journal	Combinatorica
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/s00493-004-0004-0
Publication status	Published - 1 Jan 2004

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abstract = "It is proved that any subset A of (ℤ/2ℤ)n, having k elements, such that |A+A|=c|A| (with c<4), is contained in a subgroup of order at most u-1k where u = u(c) > 0 is an explicit function of c which does not depend on k nor on n. This improves by a radically different method the corresponding bounds deduced from a more general result of I. Z. Ruzsa.",

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N2 - It is proved that any subset A of (ℤ/2ℤ)n, having k elements, such that |A+A|=c|A| (with c<4), is contained in a subgroup of order at most u-1k where u = u(c) > 0 is an explicit function of c which does not depend on k nor on n. This improves by a radically different method the corresponding bounds deduced from a more general result of I. Z. Ruzsa.

AB - It is proved that any subset A of (ℤ/2ℤ)n, having k elements, such that |A+A|=c|A| (with c<4), is contained in a subgroup of order at most u-1k where u = u(c) > 0 is an explicit function of c which does not depend on k nor on n. This improves by a radically different method the corresponding bounds deduced from a more general result of I. Z. Ruzsa.

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EP - 68

JO - Combinatorica

JF - Combinatorica

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On small sumsets in (ℤ/2ℤ)n

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On small sumsets in (ℤ/2ℤ)ⁿ