# additive basis

A subset $A$ of $\mathbb{Z}$ is an *() basis* of $n$ if

$$nA=\mathbb{N}\cup \{0\},$$ |

where $nA$ is $n$-fold sumset of $A$. Usually it is assumed that $0$ belongs to $A$ when saying that $A$ is an additive basis.

Title | additive basis |
---|---|

Canonical name | AdditiveBasis |

Date of creation | 2013-03-22 13:19:17 |

Last modified on | 2013-03-22 13:19:17 |

Owner | bbukh (348) |

Last modified by | bbukh (348) |

Numerical id | 6 |

Author | bbukh (348) |

Entry type | Definition |

Classification | msc 11B13 |

Synonym | basis |

Related topic | AsymptoticBasis |

Related topic | SchnirlemannDensity |

Related topic | EssentialComponent |

Defines | order of additive basis |