Optimally small sumsets in finite abelian groups

Shalom Eliahou; Michel Kervaire; Alain Plagne

doi:10.1016/S0022-314X(03)00060-X

Optimally small sumsets in finite abelian groups

Shalom Eliahou
, Michel Kervaire
, Alain Plagne

Université du Littoral Côte d'Opale
University of Geneva

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

Let G be a finite abelian group of order g. We determine, for all 1 ≤r,s≤g, the minimal size μ_G(r,s) = min A + B of sumsets A + B, where A and B range over all subsets of G of cardinality r and s, respectively. We do so by explicit construction. Our formula for μ_G(r,s) shows that this function only depends on the cardinality of G, not on its specific group structure. Earlier results on μ_G are recalled in the Introduction.

langue originale	Anglais
Pages (de - à)	338-348
Nombre de pages	11
journal	Journal of Number Theory
Volume	101
Numéro de publication	2
Les DOIs	https://doi.org/10.1016/S0022-314X(03)00060-X
état	Publié - 1 août 2003

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10.1016/S0022-314X(03)00060-X

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abstract = "Let G be a finite abelian group of order g. We determine, for all 1 ≤r,s≤g, the minimal size μG(r,s) = min A + B of sumsets A + B, where A and B range over all subsets of G of cardinality r and s, respectively. We do so by explicit construction. Our formula for μG(r,s) shows that this function only depends on the cardinality of G, not on its specific group structure. Earlier results on μG are recalled in the Introduction.",

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KW - Additive number theory

KW - Cauchy-Davenport theorem

KW - Initial segment

KW - Kneser theorem

KW - Sumset

U2 - 10.1016/S0022-314X(03)00060-X

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ER -

Optimally small sumsets in finite abelian groups

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