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

Abstract

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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.

How to cite

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Vsevolod 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

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  1. [1] G. Freiman, On addition of finite sets, I, Izv. Vyssh. Uchebn. Zaved. Mat. 1959 (6), 202-213. Zbl0096.25904
  2. [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. [3] M. Kneser, Abschätzung der asymptotischen Dichte von Summenmengen, Math. Z. 58 (1953), 459-484. Zbl0051.28104
  4. [4] M. Kneser, Ein Satz über abelschen Gruppen mit Anwendungen auf die Geometrie der Zahlen, Math. Z. 61 (1955), 429-434. Zbl0064.04305
  5. [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. 

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