# sumset

Let ${A}_{1},{A}_{2},\mathrm{\dots},{A}_{n}$ be subsets of an additive group^{} $G$. The sumset

$${A}_{1}+{A}_{2}+\mathrm{\cdots}+{A}_{n}$$ |

is the set of all elements of the form ${a}_{1}+{a}_{2}+\mathrm{\cdots}+{a}_{n}$, where ${a}_{i}\in {A}_{i}$.

In geometry a sumset is often called *Minkowski sum ^{}*.

Title | sumset |
---|---|

Canonical name | Sumset |

Date of creation | 2013-03-22 13:19:14 |

Last modified on | 2013-03-22 13:19:14 |

Owner | bbukh (348) |

Last modified by | bbukh (348) |

Numerical id | 5 |

Author | bbukh (348) |

Entry type | Definition |

Classification | msc 11B13 |

Classification | msc 11B05 |

Synonym | Minkowski sum |

Related topic | MinkowskiSum2 |