Freiman’s theorem

Let $A$ be a finite set of integers such that the $2$ -fold sumset $2A$ is “small”, i.e., $|2A|<c|A|$ for some constant $c$ . There exists an $n$ -dimensional arithmetic progression (http://planetmath.org/MulidimensionalArithmeticProgression) of length $c^{\\prime}|A|$ that contains $A$ , and such that $c^{\\prime}$ and $n$ are functions of $c$ only.

References

1 Melvyn B. Nathanson. Additive Number Theory: Inverse Problems and Geometry ofSumsets, volume 165 of GTM. Springer, 1996. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0859.11003Zbl 0859.11003.

单词	FreimansTheorem
释义	Freiman’s theorem Let $A$ be a finite set of integers such that the $2$ -fold sumset $2A$ is “small”, i.e., $\|2A\|<c\|A\|$ for some constant $c$ . There exists an $n$ -dimensional arithmetic progression (http://planetmath.org/MulidimensionalArithmeticProgression) of length $c^{\\prime}\|A\|$ that contains $A$ , and such that $c^{\\prime}$ and $n$ are functions of $c$ only. References 1 Melvyn B. Nathanson. Additive Number Theory: Inverse Problems and Geometry ofSumsets, volume 165 of GTM. Springer, 1996. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0859.11003Zbl 0859.11003.
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