# system of distinct representatives

Let $S=\{{S}_{1},{S}_{2},\mathrm{\dots}{S}_{n}\}$ be a finite collection^{} of finite sets^{}. A *system of distinct representatives*, or *SDR*, of $S$ is a set

$${x}_{1}\in {S}_{1},{x}_{2}\in {S}_{2},\mathrm{\dots}{x}_{n}\in {S}_{n}$$ |

such that

$${x}_{i}\ne {x}_{j}\text{whenever}i\ne j$$ |

(i.e., each choice must be unique).

Title | system of distinct representatives |
---|---|

Canonical name | SystemOfDistinctRepresentatives |

Date of creation | 2013-03-22 12:35:11 |

Last modified on | 2013-03-22 12:35:11 |

Owner | vampyr (22) |

Last modified by | vampyr (22) |

Numerical id | 4 |

Author | vampyr (22) |

Entry type | Definition |

Classification | msc 05D15 |

Synonym | SDR |