# polymatroid

The *polymatroid* defined by a given matroid $(E,r)$ is the set of
all functions $w:E\to \mathbb{R}$ such that

$$w(e)\ge 0\mathit{\hspace{1em}\hspace{1em}}\text{for all}e\in E$$ |

$$\sum _{e\in S}w(e)\le r(S)\mathit{\hspace{1em}\hspace{1em}}\text{for all}S\subset E.$$ |

Polymatroids are related to the convex polytopes seen in linear programming,
and have similar^{} uses.

Title | polymatroid |
---|---|

Canonical name | Polymatroid |

Date of creation | 2013-03-22 13:56:43 |

Last modified on | 2013-03-22 13:56:43 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 4 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 05B35 |