## Greedoids |

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### Contents

Table of Contents | 1 |

Abstract Linear Dependence Matroids | 10 |

Submodular Functions and Polymatroids | 17 |

Copyright | |

15 other sections not shown

### Common terms and phrases

accessible set system assume balanced interval greedoid basic word basis bisimplicial characterization closed under union closure feasible closure operator combinatorial Consider contains contradicting Conversely convex geometry convex hull convex sets Corollary critical circuit define denote directed graph edge element x e equivalent exchange property exists an element feasible sets feasible subset feasible words Gauss greedoid Gaussian elimination greedy algorithm ground set Hence hereditary language homotopy implies independence system induction intersection interval greedoid interval property isomorphic k-connected Lemma linear matroid maximal element minimal monotone nodes objective function optimal ordered geometry ordered set partially ordered set path polymatroid greedoid poset antimatroid poset greedoid Proof r(X U rank feasible sets rank function satisfies Section semimodular lattice set system simplicial submodular Suppose Theorem topological transposition property undirected branching greedoid unique vertex X G E X U Y X1 O X2