# Freiman’s theorem

Let $A$ be a finite set^{} of integers such that the $2$-fold sumset $2A$ is “small”, i.e., $$ 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 of Sumsets, volume 165 of GTM. Springer, 1996. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0859.11003Zbl 0859.11003.

Title | Freiman’s theorem |
---|---|

Canonical name | FreimansTheorem |

Date of creation | 2013-03-22 13:39:05 |

Last modified on | 2013-03-22 13:39:05 |

Owner | bbukh (348) |

Last modified by | bbukh (348) |

Numerical id | 7 |

Author | bbukh (348) |

Entry type | Theorem |

Classification | msc 11B25 |