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Optimally small sumsets in finite abelian groups |
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| Authors: | Shalom Eliahou Michel Kervaire |
| Affiliation: | a Département de Mathématiques, LMPA Joseph Liouville, Université du Littoral Côte d'Opale, Bâtiment Poincaré, 50, rue Ferdinand Buisson, B.P. 699, FR-62228 Calais, France b Département de Mathématiques, Université de Genève, 2-4, rue du Lièvre, B.P. 240, 1211 Genève 24, Switzerland c LIX, École polytechnique, 91128 Palaiseau Cedex, France |
| 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. |
| Keywords: | Primary: 11B75, 20D60 20K01 Secondary: 05A05, 11P70 |
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