On addition of two distinct sets of integers

• Autorzy: Vsevolod F. Lev , Pavel Y. Smeliansky
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 70
• Numer: 1
• Strony: 85-91

Daty

wydano

1995

otrzymano

1994-05-06

poprawiono

1994-07-12

Twórcy

autor

Vsevolod F. Lev

• School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978 Tel-Aviv, Israel

autor

Pavel Y. Smeliansky

• 2/56 Smith Str., Wollongong, New South Wales 2000, Australia

Bibliografia

• [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.