# On addition of two distinct sets of integers

Vsevolod F. Lev; Pavel Y. Smeliansky

Acta Arithmetica (1995)

- Volume: 70, Issue: 1, page 85-91
- ISSN: 0065-1036

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topVsevolod F. Lev, and Pavel Y. Smeliansky. "On addition of two distinct sets of integers." Acta Arithmetica 70.1 (1995): 85-91. <http://eudml.org/doc/206738>.

@article{VsevolodF1995,

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.},

author = {Vsevolod F. Lev, Pavel Y. Smeliansky},

journal = {Acta Arithmetica},

keywords = {set addition; doubling; inverse problems; additive number theory; addition of distinct sets},

language = {eng},

number = {1},

pages = {85-91},

title = {On addition of two distinct sets of integers},

url = {http://eudml.org/doc/206738},

volume = {70},

year = {1995},

}

TY - JOUR

AU - Vsevolod F. Lev

AU - Pavel Y. Smeliansky

TI - On addition of two distinct sets of integers

JO - Acta Arithmetica

PY - 1995

VL - 70

IS - 1

SP - 85

EP - 91

AB - 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.

LA - eng

KW - set addition; doubling; inverse problems; additive number theory; addition of distinct sets

UR - http://eudml.org/doc/206738

ER -

## References

top- [1] G. Freiman, On addition of finite sets, I, Izv. Vyssh. Uchebn. Zaved. Mat. 1959 (6), 202-213. Zbl0096.25904
- [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. Zbl0156.05102
- [3] M. Kneser, Abschätzung der asymptotischen Dichte von Summenmengen, Math. Z. 58 (1953), 459-484. Zbl0051.28104
- [4] M. Kneser, Ein Satz über abelschen Gruppen mit Anwendungen auf die Geometrie der Zahlen, Math. Z. 61 (1955), 429-434. Zbl0064.04305
- [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.

## Citations in EuDML Documents

top- Yonutz Stanchescu, On addition of two distinct sets of integers
- Yonutz Stanchescu, On the structure of sets with small doubling property on the plane (I)
- Yong-Gao Chen, On addition of two sets of integers
- Oriol Serra, Gilles Zémor, Large sets with small doubling modulo $p$ are well covered by an arithmetic progression

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