# multidimensional arithmetic progression

An $n$-dimensional arithmetic progresssion is a set of the form

$Q$ | $=Q(a;{q}_{1},\mathrm{\dots},{q}_{n};{l}_{1},\mathrm{\dots},{l}_{n})$ | ||

$$ |

The length of the progression is defined as ${l}_{1}\mathrm{\cdots}{l}_{n}$. The progression is *proper* if $|Q|={l}_{1}\mathrm{\cdots}{l}_{n}$.

## 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 | multidimensional arithmetic progression |
---|---|

Canonical name | MultidimensionalArithmeticProgression |

Date of creation | 2013-03-22 13:39:02 |

Last modified on | 2013-03-22 13:39:02 |

Owner | bbukh (348) |

Last modified by | bbukh (348) |

Numerical id | 7 |

Author | bbukh (348) |

Entry type | Definition |

Classification | msc 11B25 |

Synonym | generalized arithmetic progression |

Related topic | ArithmeticProgression |