## Combinatorial GeometriesA continuation of The Theory of Matroids, (edited by N. White), this volume consists of a series of related surveys by top authorities on coordinatizations, matching theory, transversal and simplicial matroids, and studies of important matroid variants. An entire chapter is devoted to matroids in combinatorial optimization, a topic of current interest. Care has been taken to ensure a uniform style throughout, and to make a work that can be used as a reference or as a graduate textbook. Excercises are included. |

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### Contents

Matroid operations | 6 |

Brackets | 15 |

Coordinatizations over transcendental extensions | 21 |

Binary Matroids J C Fournier | 28 |

Unimodular Matroids Neil White | 40 |

Introduction to Matching Theory Richard A Brualdi | 53 |

Transversal Matroids Richard A Brualdi | 72 |

Simplicial Matroids Raul Cordovil and Bernt Lindstrdm | 98 |

Whitney Numbers Martin Aigner | 139 |

### Common terms and phrases

algebraic assume base orderable basis of M(S binary matroids bipartite graph Brualdi Brylawski characteristic polynomial chromatic polynomial circuits class of matroids cocircuit cographic columns Combinatorial Geometries construction contains coordinatizable coordinatization copoints Corollary corresponding Crapo critical exponent cyclic flats define denote disjoint dual edges Edmonds elements entries equivalent example exists field follows geometric lattice given graph G graphic matroids greedy algorithm ground set rank Hence Homotopy Theorem hyperplane implies independent set induction Ingleton integral matroid lattice of rank Lemma Let M(S matching of F Math matrix matroid intersection matroid M(S matroid of rank matroid theory maximal presentation Mobius function modular nodes non-zero obtain optimization problem partial transversal path presentation of M(S Prove respect result Rota satisfies set rank function simplicial matroids spanning strict Menger matroids submodular function submodular system subspace supermodular suppose Theorem transversal matroid Tutte Tutte's unimodular matroids vector space vertex vertices Whitney numbers zonotope