## Combinatorial GeometriesThis book is a continuation of Theory of Matroids (also edited by Neil White), and again consists of a series of related surveys that have been contributed by authorities in the area. The volume begins with three chapters on coordinatisations, followed by one on matching theory. The next two deal with transversal and simplicial matroids. These are followed by studies of the important matroid invariants. The final chapter deals with matroids in combinatorial optimisation, a topic of much current interest. The whole volume has been carefully edited to ensure a uniform style and notation throughout, and to make a work that can be used as a reference or as an introductory textbook for graduate students or non-specialists. |

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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 |

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### 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