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ArticleOriginal scientific text

Title

On addition of two distinct sets of integers

Authors 1, 2

Affiliations

  1. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978 Tel-Aviv, Israel
  2. 2/56 Smith Str., Wollongong, New South Wales 2000, Australia

Abstract

What is the structure of a pair of finite integers sets A,B ⊂ ℤ with the small value of |A+B|? We answer this question for addition coefficient 3. The obtained theorem sharpens the corresponding results of G. Freiman.

Bibliography

  1. G. Freiman, On addition of finite sets, I, Izv. Vyssh. Uchebn. Zaved. Mat. 1959 (6), 202-213.
  2. G. Freiman, Inverse problems of additive number theory, VI. On addition of finite sets, III, Izv. Vyssh. Uchebn. Zaved. Mat. 1962 (3), 151-157.
  3. M. Kneser, Abschätzung der asymptotischen Dichte von Summenmengen, Math. Z. 58 (1953), 459-484.
  4. M. Kneser, Ein Satz über abelschen Gruppen mit Anwendungen auf die Geometrie der Zahlen, Math. Z. 61 (1955), 429-434.
  5. J. Steinig, On Freiman's theorems concerning the sum of two finite sets of integers, in: Preprints of the conference on Structure Theory of Set Addition, CIRM, Marseille, 1993, 173-186.
Acta Arithmetica
1995/70/1
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Pages:
85-91
Main language of publication
English
Received
1994-05-06
Accepted
1994-07-12
Published
1995
Exact and natural sciences